SPEECH enhancement (SE) aims to improve the quality and intelligibility of distorted speech signals, which may be caused by background noises, interference and recording devices. SE approaches are commonly used as pre-processing in various audio-related applications, such as speech communication 
, automatic speech recognition (ASR)[2, 3, 4], speaker recognition [5, 6], hearing aids [7, 8, 9, 10], and cochlear implants [11, 12, 13]. Traditional SE algorithms design the denoising model based on statistical properties of speech and noise signals. One class of SE algorithms computes a filter to generate clean speech by reducing noise components from the noisy speech signals. Essential approaches include spectral subtraction , Wiener filtering , and minimum mean square error (MMSE) 
. Another class of SE algorithms adopts a subspace structure to separate the noisy speech into noisy and clean speech subspaces, and the clean speech is restored based on the information in the clean speech subspace. Well-known approaches belonging to this category include singular value decomposition (SVD), generalized subspace approach with pre-whitening, Karhunen-Loeve transform (KLT) 
, and principal component analysis (PCA)
. Despite being able to yield satisfactory performance under stationary noise conditions, the performance of these approaches is generally limited under non-stationary noise conditions. A major reason is that traditional signal processing-based solutions cannot accurately estimate noise components, consequently causing musical noises and suffering significant losses in both quality and intelligibility of enhanced speech.
Recent work has seen the emergence of machine learning and deep learning-based SE methods. Different from traditional methods, machine learning-based SE methods prepare a model based on training data in a data-driven manner without imposing strong statistical constraints. The prepared model is used to transform noisy speech signals to clean speech signals. Well-known machine learning-based models include non-negative matrix factorization, compressive sensing , sparse coding , , and robust principal component analysis (RPCA) . Deep learning models have drawn great interest due to their outstanding nonlinear mapping capabilities. Based on the training targets, deep learning-based SE models can be divided into two categories: masking-based and mapping-based. The masking-based methods compute masks describing the time-frequency relationships of clean speech and noise components. Various types of masks have been derived, e.g., ideal binary mask (IBM) , ideal ratio mask (IRM) , target binary mask , spectral magnitude mask  and phase sensitive mask . The mapping-based methods, on the other hand, treat the clean spectral magnitude representations as the target and aim to calculate a transformation function to map noisy speech directly to the clean speech signal. Well-known examples are the fully connected neural network , deep denoising auto-encoder (DDAE) [31, 32]
, convolutional neural network (CNN)
, and long-short-term memory (LSTM) along with its combinations[34, 35].
Although deep learning-based methods can provide outstanding performance when dealing with seen noise types (the noise types involved in the training data), the denoising ability is notably reduced when unseen noise types (the noise types not involved in the training data) are encountered. In real-world applications, it is not guaranteed that an SE system always deals with seen noise types. This may limit the applicability of deep learning-based SE methods. Moreover, since the SE model is trained by training data including a variety of noise types, the enhancement performance for a particular noise type (even if involved in the training data) can be weakened. In this study, we intend to design a new framework to increase deep learning SE model generalizability, i.e., to improve the enhancement performance for both seen and unseen noise types.
Ensemble learning algorithms have proven to effectively improve the generalization capabilities of different machine learning tasks. Examples include acoustic modeling [36, 37], image classification , and bio-medical analysis . Ensemble learning algorithms have also been used for speech signal processing, e.g., speech dereverberation  and SE. Lu et al. investigated ensemble learning using unsupervised partitioning of training data . Kim, on the other hand, proposed an online selection from trained models. The modular neural network (MNN) consists of two consecutive DNN modules: the expert module that learns specific information (e.g. SNRs, noise types, genders) and the arbitrator module that selects the best expert module in the online phase . In , the authors investigated a mixture-of-experts algorithm for SE, where the expert models enhance specific speech types corresponding to speech phonemes. Additionally, in [44, 45], the authors proposed a joint estimation of different targets with enhanced speech as the primary task to improve the SE performance.
Despite the aforementioned ensemble learning models having achieved notable improvements, a specific component model is generally chosen for a specific data set and may not be suitable when applied to different large or small data sets with different characteristics. Therefore, it is desirable to build a system that can dynamically determine the complexity of the ensemble structure using a common prior knowledge of speech and noise characteristics or attributes. In this study, we propose a novel denoising autoencoder with multi-branched encoder (DAEME) model for SE. A dynamically-sized decision tree (DSDT) is used to guide the DAEME model, thereby improving the generalizability of the model to various speech and noise conditions. The DSDT is built based on prior knowledge of speech and noise characteristics from a training data set. In building the DSDT, we regard the speaker gender and signal-to-nose ratio (SNR) as the utterance-level attributes and the high and low frequency components as the signal-level attributes. Based on these definitions, the training data set is partitioned into several clusters based on the degree of attributes desired. Then, each cluster is used to train a corresponding SE model (termed component model) that performs spectral mapping from noisy to clean speech. After the first phase of training, each model is considered to be a branch of the encoder in the DAEME model. Finally, a decoder is trained on top of the multiple component models. In the online stage, noisy speech is first processed by the tree and fed to each component model. The multiple outputs from these models are then integrated into the decoder to determine the final enhanced speech.
Experimental results show that DAEME is superior to conventional deep learning-based SE models not only in terms of objective evaluation metrics, but also in the ASR tests and the quality of subjective human listening tests. The results also indicate that DAEME has a better generalization ability to unseen noise types than other models compared in this paper. Compared to other ensemble-based SE algorithms, DAEME can dynamically determine the number of regressions (i.e., component models) according to the online computational constraints. We believe that this dynamic structure makes the DAEME algorithm especially suitable for real-world applications.
The rest of this paper is organized as follows. We first review several related learning-based SE approaches in Section II as our comparative baseline models. Then, we elaborate the proposed DAEME algorithm in Section III. In Section IV, we describe the experimental setup, report the experimental results, and discuss our findings. Finally, we conclude our work in Section V.
Ii Related Works
In this section, we first review some of these nonlinear mapping models along with a the pseudo-linear transform, which will be used as independent and combined models for baseline comparisons in the experiments. Then, we review the main concept and algorithms of ensemble learning. Typically, in a learning-based SE task, a set of paired training data (noisy speech and clean speech) is used to train the model. For example, given the noisy speechy, the clean speech x can be denoted as , where is a mapping function. The objective is to derive the mapping function that transforms y to x, which can be formulated as a regression function. Generally, a regression function can be linear or non-linear. As mentioned earlier, numerous deep learning models have been used for SE, e.g., deep fully connected neural network , DDAE [31, 32], RNN , LSTM [34, 35], CNN , FCN , and the combination of these models.
Ii-a SE using a linear regression function
In the linear model, the predicted weights are calculated based on a linear function of the input data with respect to the target data. More specifically, we assume the correlation of noisy speech, y, and clean speech, x, can be modeled by , where W denotes the affine transformation. The Moore-Penrose pseudo inverse , which can be calculated using an orthogonal projection method, is commonly involved to solve the large size matrix multiplication. Thus, we can have
where C denotes the scalar matrix.
On the other hand, neural network-based methods aim to minimize reconstruction errors of predicted data and reference data based on a non-linear mapping function. We will briefly describe some models adopted in this study below.
Ii-B SE using non-linear regression functions: DDAE and BLSTM
The deep denoising auto-encoder (DDAE) [31, 32] has shown impressive performance in SE. In , the DDAE maps the noisy speech spectra to the target clean speech spectra through a non-linear transformation. The front layers of DDAE first encode the log-power-spectrogram (LPS) of the input speech. Then, DDAE decodes the extracted representation to fit the LPS of the target clean speech. For example, if and represent the LPSs of paired clean speech X and noisy speech Y, then:
is a non-linear activation function,and
represent the weight matrix and bias vector for the-th layer. From (.) to
(.), the encoding-decoding process forms a non-linear regression function. As reported in, the DDAE with a highway structure, termed HDDAE, is more robust than the conventional DDAE, and thus we will focus on the HDDAE model in this study.
provide bilateral information exchange between series of parallel neurons, proving effective for dealing with temporal signals. The output activation from the previous layerand the activation of the previous time frame are concatenated as the input vector for the -th layer at time frame . The equations within a memory block, according to , can then be derived as follows:
where , , and are activation functions; denotes the Hadamard product (element-wise product). Finally, an affine transformation is applied to the final activation and of the -th layer in both directions on the time axis as:
Ii-C Ensemble learning
An ensemble learning algorithm learns multiple component models along with a fusion model that combines the complementary information from the component models. Ensemble learning has been confirmed as an effective machine learning algorithm in various regression and classification tasks . In the speech signal processing field, various ensemble learning algorithms have been derived. These algorithms can be roughly divided into three categories. For the first category, the whole training set is partitioned into subsets, and each of component models is trained by a subset of the training data. Notable examples include [36, 37, 41, 42, 50]. The second category of approaches build multiple models based on different types of acoustic features. Well-known approaches include [44, 51]. The third category constructs multiple models using different model types or structures. Successful approaches belonging to this category include [45, 52]. By exploiting complementary information from multiple models, ensemble learning approaches can yield more robust performance compared to conventional machine learning algorithms.
Despite the impressive performance in speech signal processing tasks, there are three possible limitations to implementing a typical ensemble learning model in a real-world SE application: First, the interpretability is not always clear. More specifically, it is difficult to tell the contribution of each component model. Second, the amount of training data for training multiple models may not be sufficient. Third, after the system is determined, it is difficult to change the system complexity. More specifically, the number of component models cannot be dynamically determined based on the hardware limitation and the amount of training data.
To overcome the above three limitations, we propose a novel DAEME SE algorithm, which comprises offline and online stages. In the offline stage, a DSDT is constructed based on the attributes of speech and noise acoustic features. Since the DSDT is constructed in a top-down manner, a node in a higher layer consists of speech data with broad attribute information. On the other hand, a node in a lower layer denotes the speech data with more specific attribute information. An SE model is built for each node in the tree. These models are referred to component models in the multi-branched encoder. Next, a decoder is trained in order to combine the results of the multiple models. In the online stage, a testing utterance is first processed by the component models; the outputs of these models are then combined by the decoder to generate the final output. Since the DSDT has a clear physical structure, it becomes easy to analyze the SE property of each component model. Moreover, based on the tree, we may dynamically determine the number of SE models according to the amount of training data and the hardware limitation. Last but not least, in , the authors proposed a special “over-fitting” strategy to interpret the effectiveness of a component model. The DAEME algorithm has better interpretability by using attribute-fit regressions based on the DSDT.
Iii Proposed Algorithm
The overall architecture of the proposed DAEME approach is depicted in Fig. 1. In this section, we will detail the offline and online stages.
Iii-a Offline stage
In the offline stage, we first build a tree based on the attributes of the training utterances in a top-down manner. The root of the tree includes the entire set of training data. Then, based on the utterance-level attribute, we create the branches from the root node. As the layers increase, the nodes represent more specific utterance-level attribute information. Next, we process signal-level attributes to create branches upon the nodes. Finally, we have a tree with multiple branches. As shown in Fig. 2, based on the utterance-level and signal-level attributes, we build UAT and SAT, respectively. In the following subsection, we will introduce the UAT and SAT in more details.
Iii-A1 Utterance-level attribute tree (UAT)
The utterance-level attributes include speaker and speaking environment factors, such as the gender, age, accent, or identity for the speaker factor, and the signal-to-noise ratio (SNR), noise type, and acoustic environment for the environment factor. As reported in, three major factors that affect the SE performance are the noise type, speaker, and SNR. In real-world scenarios, the noise type is usually inaccessible beforehand. Accordingly, we only consider the speaker and SNR factors when building the attribute tree in this study. The root node includes all the training utterances. Next, we create two branches from the root node for male and female speakers. Therefore, each node in the second layer contains the training utterances of male or female speakers. Then, the two nodes in the second layer are further divided to four nodes in the third layer, each containing the training data of “male with high SNR”, “male with low SNR”, “female with high SNR” or “female with low SNR”.
Iii-A2 Signal-level attribute tree (SAT)
For the signal-level attributes, we segment the acoustic features into several groups, each with similar properties. For SE, it has been reported that considering high and low frequency properties can give improved performance [55, 56]. In this study, we segment the acoustic features into high-frequency and low-frequency parts by two methods: spectral segmentation (SS) and wavelet decomposition (WD). With the signal-level attributes, we can create an additional layer for each node of the tree constructed using the utterance-level attributes, forming final binary branches from each node.
Iii-A3 Models of multi-branched encoder and decoder
The overall procedure of the offline stage is shown in Fig. 1 (a). We estimate a component model for each node in the tree. The input and output of the model is paired by noisy and clean features, and the objective is to estimate the mapping function between the paired features. We reason that the model at the highest layer (the root node) characterizes the mapping function globally, rather than considering specific local information independently. In our case, the local information includes the speaker attributes and environment features segmented by each layer and node in the dynamic attribute tree. On the other hand, the model corresponding to a node in a lower layer characterizes a more localized mapping of paired noisy and clean features. More specifically, each model characterizes a particular mapping in the overall acoustic space. Given the component SE models, we then estimate a decoder. Note that by using the component models to build multiple SE mapping functions, we can factorize the global mapping function (the mapping of the root node in our system) into several local mapping functions; the decoder uses the complementary information provided by the local mappings to obtain improved performance as compared to the global mapping. This also follows the main concept of ensemble learning: building multiple over-trained models, each specializing in a particular task, and then computing a fusion model to combine the complementary information from the multiple models. The system can be derived with the component models as
and the decoder as
where , y, j, and k represents the enhanced speech, input noisy speech, UAT node index, and SAT node index, respectively. The decoder combines the information from the multiple models, and the parameter of is entitled by:
where x denotes the clean speech.
Iii-B Online stage
The online stage of the DAEME algorithm is shown in Fig. 1 (b). The input speech is first converted to acoustic features, and each component model processes these features separately. The outputs are then combined with a decoder. Finally, the enhanced acoustic features are reconstructed to form the speech waveform. As mentioned earlier, based on the tree structure, we may dynamically determine the number of ensemble models according to the hardware limitation or the amount of training data available.
It is important to note that one can use different types of models and different types of acoustic features to form the component models in the multi-branched encoder. In this study, we intend to focus on comparing the effects caused by different attributes of the speech utterances, so the same NN model architecture was used for all components in the multi-branched encoder. Additionally, we adopted different types of models to form encoders and decoders to investigate the correlation between the model types and the overall performance.
Iv Experiments & Results
We used two datasets to evaluate the proposed algorithm, namely the Wall Street Journal (WSJ) corpus  and the Taiwan Mandarin version of the hearing in noise test (TMHINT) sentences . In this section, we present the experimental setups for the two datasets and discuss the evaluation results.
Iv-a Evaluation metrics
To evaluate the performance of SE algorithms, we used Perceptual Evaluation of Speech Quality (PESQ)  and Short-Time Objective Intelligibility (STOI) . PESQ and STOI have been widely used as standard objective measurement metrics in many related tasks [30, 61, 62, 63, 64, 65, 66, 67, 68, 69, 44, 70, 71]. PESQ specifically aims to measure the speech quality of the utterances, while STOI aims to evaluate the speech intelligibility. The PESQ score ranges from -0.5 to 4.5, a higher score indicating better speech quality. The STOI score ranges from 0.0 to 1.0, a higher score indicating higher speech intelligibility.
Iv-B Experiments on the WSJ dataset
The WSJ corpus is a large vocabulary continuous speech recognition (LVCSR) benchmark corpus, which consists of 37,416 training and 330 test clean speech utterances. The utterances were recorded at a sampling rate of 16Khz. We prepared the noisy training data by artificially contaminating the clean training utterances with 100 types of noises at 30 SNR levels (20dB to -10dB, with a step of 1dB). Each clean training utterance was contaminated by one randomly selected noise condition; therefore, the entire training set consisted of 37,416 noisy-clean utterance pairs. To prepare the noisy test data, four types of noises, including two stationary types (i.e., car and pink) and two non-stationary types (i.e., street and babble), were added to the clean test utterances at seven SNR levels (-15 dB, -10 dB, -5dB, 0 dB, 5 dB, 10 dB, and 15 dB). Note that the four noise types used to prepare the test data were not involved in preparing the training data. We extracted acoustic features by applying 512-point Short-time Fourier Transform (STFT) with a Hamming window size of 32 ms and a hop size of 16 ms on training and test utterances, creating 257-point STFT log-power-spectrum (LPS) features. For the baseline SE system, we used a bidirectional long short-term memory (BLSTM) model with two bidirectional LSTM layers of 300 nodes followed by a fully connected output layer. For DAEME, similar to the baseline system, we used two bidirectional LSTM layers with 300 nodes and one fully connected output layer to form the components in the multi-branched encoder. Since an essential objective of DAEME is to provide sufficient information to be able to generalize the acoustic models, multiple models are created, each learning the particular information to be finally mapped in the decoder. A CNN composed of three convolutional layers and two fully connected layers, each convolutional layer containing 64 channels and each fully connected layers containing 1024 neurons, was used to form the decoder.
Iv-C Prior knowledge of speech and noise structures
Recent monaural SE studies have mentioned the importance of attributive generalizability in SE systems. For example, in , Morten, et al. compared noise types, speaker, and SNR level and their potential to enhance the intelligibility of SE systems. To build the DSDT and the corresponding DAEME system, we first qualitatively analyzed the acoustic properties of speech attributes. As mentioned earlier, we assumed that the noise type is inaccessible and thus only conducted the analysis using the training data of the WSJ dataset and applied T-SNE analysis  on the LPS features of the complete set of training data. The analysis results are shown in Fig. 3, where in Fig. 3 (a), we analyzed the gender attributes, and in Fig. 3 (b) and (c), we analyzed the SNR attributes.
From Fig. 3 (a), we can note a clear separation between male (yellow dots) and female (purple dots). In Figs. 3 (b) (i.e., male data of different SNR levels) and 3 (c) (i.e., female data of different SNR levels), the T-SNE analysis also shows a clear separation between high SNR (10dB and above, yellow dots) and low SNR (below 10dB, purple dots) in both gender partitions.
On the other hand, from the signal point of view, most real-world noises were non-stationary in the time-frequency domain. This suggests that noise pollution is unlikely to occur in all frequency bands at the same time even under low SNR conditions. In our previous studies, segmental frequency bands were proposed to enhance speaker adaptation. In this study, the signal-level attribute is used to consider the high and low frequency bands. With the signal-level attribute, the SE algorithm can obtain more speech structure information even when some time-frequency regions of speech are heavily contaminated by noises.
Iv-C1 The effectiveness of the UAT
We first analyzed the DAEME model with a tree built with the utterance-level attributes. As mentioned in Section III-A-1), the root node of the UAT included the entire set of 37,416 noisy-clean utterance pairs for training. The entire training set was divided into male and female in the first layer, each with 18,722 (male) and 18,694 (female) noisy-clean training pairs, respectively. For the next layer, the gender-dependent training data was further divided into high and low SNR conditions. Finally, there were four leaf nodes in the tree, each with 6,971 (female with high SNR), 11,723 (female with low SNR), 7,065 (male with high SNR), and 11,657 (male with low SNR) noisy-clean training pairs. We investigated the performance of DAEME with different numbers of components in the multi-branched encoder, and thus built three systems. The first system had two component models: male and female. The second system had four component models: female with high SNR, female with low SNR, male with high SNR, and male with low SNR. The third system had six component models: female, male, female with high SNR, female with low SNR, male with high SNR, and male with low SNR. The three systems are termed DAEME-UAT, DAEME-UAT, and DAEME-UAT, respectively.
In the first set of experiments, we examined the effectiveness of the UAT-based DAEME systems versus single model SE algorithms. We selected BLSTM and HDDAE for their benchmark performance in prior studies. These models were trained with the entire set of 37,416 noisy-clean utterance pairs. Fig. 4 shows the PESQ scores of the proposed systems (DAEME-UAT, DAEME-UAT, DAEME-UAT) and the single models (BLSTM and HDDAE). Fig. 5 shows the STOI scores. In these two figures, each bar indicates an average score over six SNR levels for a particular noise type. From the results in Figs. 4 and 5, we note that all the DAEME-UAT models outperform the two single model methods in all noise types. Using only the UAT, the DAEME systems already surpasses the performance of the single model SE methods by a notable margin. This result justifies the tree-based data partitioning in training the DAEME method.
To further verify the effectiveness of the UAT, we constructed another tree. The root node also contained the entire set of 37,416 noisy-clean utterance pairs. The training utterance pairs were randomly divided into two groups to form two nodes in the second layer, where each node contained 18,694 and 18,722 noisy-clean utterance pairs, respectively. In the third layer, the training utterance pairs of each node in the second layer were further divided into two groups randomly to form four nodes in the third layer. Based on this tree, we built three systems, termed DAEME-RT, DAEME-RT, and DAEME-RT, each consisting of 2, 4, and 6 component models, respectively. Figs. 6 and 7 compare the PESQ and STOI scores of different DAEME systems (including DAEME-UAT, DAEME-UAT, DAEME-UAT, DAEME-RT, DAEME-RT, and DAEME-RT) based on a knowledge-based tree (i.e., the UAT) or a random tree (the RT). From the figures, we can draw two observations. First, both DAEME-UAT and DAEME-RT achieve better performance than their respective counterparts with less component models. Second, the results of DAEME-UAT are consistently better than DAEME-RT for . The result confirms the effectiveness of the UAT over the random tree. For ease of further comparison, we list the detailed PESQ and STOI scores of DAEME-UAT (the best system in Figs 6 and 7) in Tables II and II.
Iv-C2 The effectiveness of the SAT
As introduced in Section III-A-2), we can use the SS and WD approaches to build the SAT. To compare the SS and WD approaches, we used the SAT on top of DAEME-UAT, which achieved the best performance in Fig. 6 (PESQ) and Fig. 7 (STOI), to build two systems: DAEME-USAT and DAEME-USAT, where USAT denotes the system using the “UA+SA” tree. Because the SA tree was built into each node of the UA tree, the total number of component models for an DAEME-USAT system is the number of nodes in the UA tree multiplied by the number of nodes in the SA tree. We applied the SS and WD approaches to segment the frequency bands. In either way, the SA tree had two nodes. Therefore, we obtained DAEME-USAT and DAEME-USAT based on DAEME-UAT after applying the SA trees constructed by the SS and WD approaches.
The PESQ and STOI scores of DAEME-USAT and DAEME-USAT are listed in Tables IV and IV, respectively. From these two tables, we observe that DAEME-USAT outperformed DAEME-USAT in terms of the PESQ score across 15dB to -10dB SNR conditions, while the two systems achieved comparable performance in terms of the STOI score. Comparing the results in Tables I and II and the results in Tables III and IV, we note that both DAEME-USAT and DAEME-USAT achieved better PESQ and STOI scores than DAEME-UAT. The result confirms the effectiveness of the SA tree.
Iv-D Experiments on the TMHINT dataset
The TMHINT corpus consists of speech utterances of eight speakers (four male and four female), each utterance corresponding to a sentence of ten Chinese characters. The speech utterances were recorded in a recording studio at a sampling rate of 16 kHz. Among the recorded utterances, 1,200 utterances pronounced by three male and three female speakers were used for training. 120 utterances pronounced by another two speakers (one male and one female) were used for testing. There is no overlap between the training and testing speakers and speech contents. We used 100 different noise types to prepare the noisy training data at 30 SNR levels (from -10dB to 20 dB, with a step of 1 dB). Each clean utterance was contaminated by several randomly selected noise conditions (one condition corresponds to a specific noise type and an SNR level). Finally, we collected 120,000 noisy-clean utterance pairs for training. For the testing data, four types of noises, including two stationary types (i.e., car and pink) and two non-stationary types (i.e., street and babble), were used to artificially generate noisy speech utterances at seven SNR levels (-15 dB, -10 dB, -5dB, 0 dB, 5 dB, 10 dB, and 15 dB). As with the setup for the WSJ task, these four noise types were not included in preparing the training set.
As we have evaluated the DAEME systems in several different aspects in the previous subsection, we will examine the DAEME algorithm in other aspects (including the achievable performance for seen noise types, different component model types, different decoder model types, and the ASR and listening test results) in this subsection. First, we examine the DAEME effectiveness under seen noise conditions. We prepare testing data that involved two noise types (Cafeteria and Crowd) that have been included in the training set. Then, we test the enhancement performance of DAEME on these two noisy data, and the PESQ and STOI results are listed in in VI and VI, respectively. For comparison, we also listed the results of HHDAE.
We analyzed the compatibility of the DAEME algorithm with different component models. In the previous experiments, we used BLSTM to build the multi-branched encoder and CNN as the decoder. First, we followed the setup of the best model DAEME-USAT and adopted HDDAE instead of BLSTM as the architecture of a component model. In the original setting, the BLSTM model consisted of two layers, with 300 memory cells in each layer, and the CNN model composed of three convolutional layers and two fully connected layers, each convolutional layer containing 64 channels and each fully connected layers containing 1,024 neurons. The HDDAE model consisted of five hidden layers, each containing 2,048 neurons, and one highway layer . Second, we investigated the decoder. In addition to CNN, we evaluated the linear regression and the best first (BF) approach.
Iv-D1 The component models of the multi-branched encoder
Figs. 8 and 9 present the PESQ and STOI scores of different systems, including two single model SE systems (HDDAE, and BLSTM) and two DAEME-based ensemble systems, (BLSTM)DAEME, and (HDDAE)DAEME, where BLSTM, and HDDAE were used to build the component models in the multi-branched encoder, respectively. From the figures, we can note that (HDDAE)DAEME, and (BLSTM)DAEME outperform their single model counterparts (HDDAE and BLSTM). It is also shown that among the two single model-based systems, BLSTM outperformed HDDAE. Among the two DAEME-based systems, (BLSTM)DAEME achieves the best performance, suggesting that the architecture of the component model of DAEME indeed affects the overall performance.
Iv-D2 The architecture of decoder
Next, we investigated the decoder in the DAEME-based systems. In this set of experiments, BLSTM with the same architecture as in the previous experiments was used to build the component SE models. We compared three types of decoder: the CNN model used in the previous experiments and the linear regression as shown in Eq.(1). We also used the BF approach as another decoder format, which selects the most suitable output from the component models as the final output. More specifically, we assume that the gender and SNR information were accessible for each testing utterance, and the BF approach simply selected the best output without further processing. The results of using different encoder types are listed in Figs. 10 and 11, which report the PESQ and STOI scores, respectively. For the DAEME(LIN), the decoder is formed by a linear regression function, for DAEME(NON-LIN), the decoder is formed by a nonlinear mapping function based on CNN, and for DAEME(BF), the decoder is formed by the BF mechanism. From Figs. 10 and 11, it is clear that DAEME(NON-LIN) outperforms DAEME(LIN) and DAEME(BF) consistently. The results confirm that when using a decoder that has more powerful nonlinear mapping capability, the DAEME can achieve better performance.
Iv-D3 ASR performance
The previous experiments have demonstrated the ability of the DAEME methods to enhance the PESQ and STOI scores. Here, we evaluated the applicability of DAEME as a denoising front end for automatic speech recognition (ASR) under noisy conditions. Google ASR  was adopted to test the character error rate (CER) with the correct transcription reference. The best setup of DAEME for the TMHINT dataset, i.e., DAEME-USAT, was used to pre-process the input noisy speech, and the enhanced speech was sent to Google ASR. The unprocessed noisy speech and the enhanced speech by a single BLSTM model were also tested for comparison. The CER results for these three experimental setups are demonstrated in Fig. 12. It is clear that the single-model BLSTM SE system is not always helpful. The enhanced speech tends to yield higher CERs than the unprocessed noisy speech while tested under higher SNR conditions (0 to 15db) and achieve only slightly lower CERs under relatively noisier conditions (-10 to 0db). On the other hand, the proposed DAEME system achieves lower CERs under lower SNR conditions (-10 to 0db) and maintains the recognition performance under higher SNR conditions (0 to 15db) as compared to the noisy speech. The average CERs of noisy, BLSTM-enhanced, and DAEME-enhanced speech across 15dB to -10dB SNR levels are 15.85%, 16.05%, and 11.4%, respectively. DAEME achieved a relative CER reduction of 28.07% (from 15.85% to 11.4%) over the unprocessed noisy speech.
Iv-D4 Listening test
In addition to the objective evaluations and ASR tests, we also invited 15 volunteers to conduct subjective listening tests. The testing conditions included two types of noises, car noise (stationary noise) and babble noise (non-stationary noise), under two different SNR levels (car: -5dB, -10dB, babble: 0dB, 5dB). We selected different SNRs for these two noise types because the car noise is more stationary and thus easier understood as compared to the babble noise, a lower SNR should be specified for the car noise than the babble noise.
First, we asked each subject to register their judgment based on the five-point scale of signal distortion (SIG) . In the SIG test, each subject was asked to provide the natural (no degradation) level after listening to an enhanced speech utterance processed by either BLSTM or DAEME. A higher score indicates that the speech signals are more natural. The results shown in Fig. 13(a) demonstrate that DAEME can yields a higher SIG score than BLSTM. We also asked the subjects to judge the background intrusiveness (BAK)  after listening to an utterance. The BAK score ranges from 1 to 5, and a higher BAK score indicates a lower level of noise artifact perceived. The BLSTM and DAEME enhanced utterances were tested for comparison. The results shown in From Fig. 13(b) clearly demonstrate that DAEME outperforms BLSTM in terms of BAK. Finally, we conducted an AB preference test  to compare the BLSTM-enhanced speech and the DAEME-enhanced speech. Each subject listened a pair of enhanced speech utterances and gave a preference score. As shown in Fig. 13(c), the DAEME significantly outperforms BLSTM in the preference test. The results in Fig. 13 (a), (b), and (c) demonstrate that, compared to BLSTM, the speech enhanced by DAEME is more natural, less noisy, and with higher quality.
This paper proposed a novel DAEME SE approach. By considering the ensemble concept, the proposed method first exploits the complimentary information based on the multi-branched encoder, and then uses a decoder to combine the complementary information for SE. We also analyzed and confirmed that the decoder using CNN-based non-linear transformation yielded better SE performance than the decoder using linear transformation and the BF approach. Compared to other learning-based SE approaches, the proposed DAEME approach has the following two advantages:
V-1 The DAEME approach yields better enhancement performance under both seen and unseen noise types than conventional learning-based SE approaches
As presented in Section III-A, the DSDT was built based on the utterance-level attributes (UA) and signal-level attributes (SA) of speech signals. The DSDT is subsequently used to establish the multi-branched encoder in the DAEME framework. From the PESQ and STOI scores, we confirmed the effectiveness of the UA tree and the USAT (UA+SA) tree over traditional deep-learning-based approaches and the system using a random tree (RT in Figs. 6 and 7). The experimental results also confirm that the proposed DAEME has effectively incorporated the prior knowledge of speech signals to attain improved enhancement performance as compared to conventional learning-based SE approaches under both seen and unseen noise types.
V-2 The DAEME architecture with a DSDT has better interpretability and can be designed according to the amount of training data and computation resource constraints
Pre-analyzing the speech attributes of the target domain using a regression tree provides informative insights into the development of the DAEME system. By using the tree map that categorized data through speech attributes, we can optimally design the architecture of the multi-branched encoder in the DAEME to strike a good balance between the achievable performance, training data, and the system complexity.
In the future, we will explore to apply the proposed DAEME to other speech signal processing tasks, such as speech dereverberation and audio separation. An algorithm that can online determine the optimal encoder architecture based on the complexity and performance also deserves further investigations. Finally, we will implement the proposed DAEME system on practical devices for real-world speech-related applications.
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