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In the context of sketching for compressive mixture modeling, we revisit existing proofs of the Restricted Isometry Property of sketching operators with respect to certain mixtures models. After examining the shortcomings of existing…

This paper establishes a sharp condition on the restricted isometry property (RIP) for both the sparse signal recovery and low-rank matrix recovery. It is shown that if the measurement matrix $A$ satisfies the RIP condition…

The columnwise Khatri-Rao product of two matrices is an important matrix type, reprising its role as a structured sensing matrix in many fundamental linear inverse problems. Robust signal recovery in such inverse problems is often…

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…

The null space property (NSP) and the restricted isometry property (RIP) are two properties which have received considerable attention in the compressed sensing literature. As the name suggests, NSP is a property that depends solely on the…

We shall show that if the restricted isometry constant (RIC) $\delta_{s+1}(A)$ of the measurement matrix $A$ satisfies $$ \delta_{s+1}(A) < \frac{1}{\sqrt{s + 1}}, $$ then the greedy algorithm Orthogonal Matching Pursuit(OMP) will succeed.…

Compressed sensing (CS) is a new signal acquisition paradigm that enables the reconstruction of signals and images from a low number of samples. A particularly exciting application of CS is Magnetic Resonance Imaging (MRI), where CS…

Compressed sensing (CS) model of complex-valued data can represent the signal recovery process of a large amount types of radar systems, especially when the measurement matrix is row-orthogonal. Based on debiased least absolute shrinkage…

We study statistical restricted isometry, a property closely related to sparse signal recovery, of deterministic sensing matrices of size $m \times N$. A matrix is said to have a statistical restricted isometry property (StRIP) of order $k$…

Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…

We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this "phase-only compressive sensing" (PO-CS) scenario, we can…

Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…

In this paper we introduce deterministic $m\times n$ RIP fulfilling $\pm 1$ matrices of order $k$ such that $\frac{\log m}{\log k}\approx \frac{\log(\log_2 n)}{\log(\log_2 k)}$. The columns of these matrices are binary BCH code vectors that…

Modern compression algorithms exploit complex structures that are present in signals to describe them very efficiently. On the other hand, the field of compressed sensing is built upon the observation that "structured" signals can be…

There are several ways to measure the compressibility of a random measure; they include general approaches such as using the rate-distortion curve, as well as more specific notions, such as the Renyi information dimension (RID). The RID…

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…

Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…

Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…

A novel compressive-sensing based signal multiplexing scheme is proposed in this paper to further improve the multiplexing gain for multiple input multiple output (MIMO) system. At the transmitter side, a Gaussian random measurement matrix…

Compressive Sensing (CS) is a new paradigm for the efficient acquisition of signals that have sparse representation in a certain domain. Traditionally, CS has provided numerous methods for signal recovery over an orthonormal basis. However,…