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Non-uniform recovery guarantees for binary measurements and infinite-dimensional compressed sensing
Due to the many applications in Magnetic Resonance Imaging (MRI), Nuclea...
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On oracle-type local recovery guarantees in compressed sensing
We present improved sampling complexity bounds for stable and robust spa...
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Thermal Source Localization Through Infinite-Dimensional Compressed Sensing
We propose a scheme utilizing ideas from infinite dimensional compressed...
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Close Encounters of the Binary Kind: Signal Reconstruction Guarantees for Compressive Hadamard Sampling with Haar Wavelet Basis
We investigate the problems of 1-D and 2-D signal recovery from subsampl...
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Multidimensional Data Tensor Sensing for RF Tomographic Imaging
Radio-frequency (RF) tomographic imaging is a promising technique for in...
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Tensor Sensing for RF Tomographic Imaging
Radio-frequency (RF) tomographic imaging is a promising technique for in...
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Improved recovery guarantees and sampling strategies for TV minimization in compressive imaging
In this paper, we consider the use of Total Variation (TV) minimization ...
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Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling
Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world inverse problems, which are typically modelled in infinite-dimensional spaces, and where the application of finite-dimensional approaches can lead to noticeable artefacts. Another typical feature of such problems is that the signals are not only sparse in some dictionary, but possess a so-called local sparsity in levels structure. Consequently, the sampling scheme should be designed so as to exploit this additional structure. In this paper, we introduce a series of uniform recovery guarantees for infinite-dimensional compressed sensing based on sparsity in levels and so-called multilevel random subsampling. By using a weighted ℓ^1-regularizer we derive measurement conditions that are sharp up to log factors, in the sense they agree with those of certain oracle estimators. These guarantees also apply in finite dimensions, and improve existing results for unweighted ℓ^1-regularization. To illustrate our results, we consider the problem of binary sampling with the Walsh transform using orthogonal wavelets. Binary sampling is an important mechanism for certain imaging modalities. Through carefully estimating the local coherence between the Walsh and wavelet bases, we derive the first known recovery guarantees for this problem.
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