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Recovering sparse signals from linear measurements has demonstrated outstanding utility in a vast variety of real-world applications. Compressive sensing is the topic that studies the associated raised questions for the possibility of a…

Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…

The compressive sensing (CS) and 1-bit CS demonstrate superior efficiency in signal acquisition and resource conservation, while 1-bit CS achieves maximum resource efficiency through sign-only measurements. With the emergence of massive…

Spatial multiplexing cameras (SMCs) acquire a (typically static) scene through a series of coded projections using a spatial light modulator (e.g., a digital micro-mirror device) and a few optical sensors. This approach finds use in imaging…

Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from…

Compressive sensing (CS) is a promising technology for realizing energy-efficient wireless sensors for long-term health monitoring. However, conventional model-driven CS frameworks suffer from limited compression ratio and reconstruction…

Compressed sensing (CS) demonstrates that sparse signals can be recovered from underdetermined linear measurements. We focus on the joint sparse recovery problem where multiple signals share the same common sparse support sets, and they are…

Compressive sensing is a novel approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate and outperforms traditional signal processing techniques in acquiring and reconstructing…

This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…

Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…

One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measurement is available to us. In many…

Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…

Compressed sensing (CS) with prior information concerns the problem of reconstructing a sparse signal with the aid of a similar signal which is known beforehand. We consider a new approach to integrate the prior information into CS via…

Compressive sensing (CS) reconstructs images from sub-Nyquist measurements by solving a sparsity-regularized inverse problem. Traditional CS solvers use iterative optimizers with hand crafted sparsifiers, while early data-driven methods…

Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…

We study the problem of reconstructing a sparse signal from a limited number of its linear projections when a part of its support is known, although the known part may contain some errors. The ``known" part of the support, denoted T, may be…

The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…

Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…

We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…