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One-bit compressed sensing (1bCS) is a method of signal acquisition under extreme measurement quantization that gives important insights on the limits of signal compression and analog-to-digital conversion. The setting is also equivalent to…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…
How to construct a suitable measurement matrix is still an open question in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit considerable…
Compressive Sensing (CS) stipulates that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based compressive sensing…
We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The…
As technology grows, higher frequency signals are required to be processed in various applications. In order to digitize such signals, conventional analog to digital convertors are facing implementation challenges due to the higher sampling…
Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…
In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Compressive sampling has great potential for making wideband spectrum sensing possible at sub-Nyquist sampling rates. As a result, there have recently been research efforts that leverage compressive sampling to enable efficient wideband…
This paper addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements. Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals…
Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples.…
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…
We consider the problem of recovering a single or multiple frequency-sparse signals, which share the same frequency components, from a subset of regularly spaced samples. The problem is referred to as continuous compressed sensing (CCS) in…
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…
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS…