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Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a…
Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…
This note complements the paper "The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing" [2]. Its purpose is to present a proof of a result stated therein concerning the recovery…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem…
Deep generative modeling has led to new and state of the art approaches for enforcing structural priors in a variety of inverse problems. In contrast to priors given by sparsity, deep models can provide direct low-dimensional…
The investigation of the effects of sparsity or sparsity constraints in signal processing problems has received considerable attention recently. Sparsity constraints refer to the a priori information that the object or signal of interest…
Support estimation (SE) of a sparse signal refers to finding the location indices of the non-zero elements in a sparse representation. Most of the traditional approaches dealing with SE problem are iterative algorithms based on greedy…
We propose a novel sparsity model for distributed compressed sensing in the multiple measurement vectors (MMV) setting. Our model extends the concept of row-sparsity to allow more general types of structured sparsity arising in a variety of…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative…
In compressed sensing, it is often desirable to consider signals possessing additional structure beyond sparsity. One such structured signal model - which forms the focus of this paper - is the local sparsity in levels class. This class has…
Weighted $\ell_1$-minimization has been studied as a technique for the reconstruction of a sparse signal from compressively sampled measurements when prior information about the signal, in the form of a support estimate, is available. In…
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random…
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…
Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this…
We consider a distributed learning setup where a sparse signal is estimated over a network. Our main interest is to save communication resource for information exchange over the network and reduce processing time. Each node of the network…
This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…