Generalized Tensor Summation Compressive Sensing Network (GTSNET): An Easy to Learn Compressive Sensing Operation

08/04/2021
by   Mehmet Yamac, et al.
8

In CS literature, the efforts can be divided into two groups: finding a measurement matrix that preserves the compressed information at the maximum level, and finding a reconstruction algorithm for the compressed information. In the traditional CS setup, the measurement matrices are selected as random matrices, and optimization-based iterative solutions are used to recover the signals. However, when we handle large signals, using random matrices become cumbersome especially when it comes to iterative optimization-based solutions. Even though recent deep learning-based solutions boost the reconstruction accuracy performance while speeding up the recovery, still jointly learning the whole measurement matrix is a difficult process. In this work, we introduce a separable multi-linear learning of the CS matrix by representing it as the summation of arbitrary number of tensors. For a special case where the CS operation is set as a single tensor multiplication, the model is reduced to the learning-based separable CS; while a dense CS matrix can be approximated and learned as the summation of multiple tensors. Both cases can be used in CS of two or multi-dimensional signals e.g., images, multi-spectral images, videos, etc. Structural CS matrices can also be easily approximated and learned in our multi-linear separable learning setup with structural tensor sum representation. Hence, our learnable generalized tensor summation CS operation encapsulates most CS setups including separable CS, non-separable CS (traditional vector-matrix multiplication), structural CS, and CS of the multi-dimensional signals. For both gray-scale and RGB images, the proposed scheme surpasses most state-of-the-art solutions, especially in lower measurement rates. Although the performance gain remains limited from tensor to the sum of tensor representation for gray-scale images, it becomes significant in the RGB case.

READ FULL TEXT

page 1

page 8

page 9

page 10

page 11

page 12

research
10/15/2018

Compressively Sensed Image Recognition

Compressive Sensing (CS) theory asserts that sparse signal reconstructio...
research
05/24/2013

Compressive Sensing of Sparse Tensors

Compressive sensing (CS) has triggered enormous research activity since ...
research
11/18/2019

Deterministic partial binary circulant compressed sensing matrices

Compressed sensing (CS) is a signal acquisition paradigm to simultaneous...
research
01/07/2019

Compressive-Sensing Data Reconstruction for Structural Health Monitoring: A Machine-Learning Approach

Compressive sensing (CS) has been studied and applied in structural heal...
research
02/07/2017

Image Reconstruction using Matched Wavelet Estimated from Data Sensed Compressively using Partial Canonical Identity Matrix

This paper proposes a joint framework wherein lifting-based, separable, ...
research
04/21/2017

Learned D-AMP: Principled Neural Network based Compressive Image Recovery

Compressive image recovery is a challenging problem that requires fast a...
research
10/14/2021

Learning a Compressive Sensing Matrix with Structural Constraints via Maximum Mean Discrepancy Optimization

We introduce a learning-based algorithm to obtain a measurement matrix f...

Please sign up or login with your details

Forgot password? Click here to reset