
Nonuniform recovery guarantees for binary measurements and infinitedimensional compressed sensing
Due to the many applications in Magnetic Resonance Imaging (MRI), Nuclea...
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On oracletype 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 InfiniteDimensional 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 1D and 2D signal recovery from subsampl...
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Multidimensional Data Tensor Sensing for RF Tomographic Imaging
Radiofrequency (RF) tomographic imaging is a promising technique for in...
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Tensor Sensing for RF Tomographic Imaging
Radiofrequency (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 infinitedimensional compressed sensing and applications to structured binary sampling
Infinitedimensional 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 wellsuited to many realworld inverse problems, which are typically modelled in infinitedimensional spaces, and where the application of finitedimensional 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 socalled 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 infinitedimensional compressed sensing based on sparsity in levels and socalled multilevel random subsampling. By using a weighted ℓ^1regularizer 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^1regularization. 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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