Related papers: On the Noise Robustness of Simultaneous Orthogonal…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
In this work, we analyze modulated sampling schemes, such as the Nyquist Folding Receiver, which are highly efficient, readily implementable, non-uniform sampling schemes that allows for the blind estimation of a narrow-band signal's…
In the Multiple Measurements Vector (MMV) model, measurement vectors are connected to unknown, jointly sparse signal vectors through a linear regression model employing a single known measurement matrix (or dictionary). Typically, the…
Current orthogonal matching pursuit (OMP) algorithms calculate the correlation between two vectors using the inner product operation and minimize the mean square error, which are both suboptimal when there are non-Gaussian noises or…
This short note studies a variation of the Compressed Sensing paradigm introduced recently by Vaswani et al., i.e. the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known. The…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all models - e.g.…
We consider the greedy algorithms for the joint recovery of high-dimensional sparse signals based on the block multiple measurement vector (BMMV) model in compressed sensing (CS). To this end, we first put forth two versions of simultaneous…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
We discuss a method for sparse signal approximation, which is based on the correlation of the target signal with a pseudo-random signal, and uses a modification of the greedy matching pursuit algorithm. We show that this approach provides…
Sparse Subspace Clustering (SSC) is one of the most popular methods for clustering data points into their underlying subspaces. However, SSC may suffer from heavy computational burden. Orthogonal Matching Pursuit applied on SSC accelerates…
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we…
Gradient inversion attacks reveal that private training text can be reconstructed from shared gradients, posing a privacy risk to large language models (LLMs). While prior methods perform well in small-batch settings, scaling to larger…
Greedy algorithms for feature selection are widely used for recovering sparse high-dimensional vectors in linear models. In classical procedures, the main emphasis was put on the sample complexity, with little or no consideration of the…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
We consider the scenario in which multiple sensors send spatially correlated data to a fusion center (FC) via independent Rayleigh-fading channels with additive noise. Assuming that the sensor data is sparse in some basis, we show that the…
This paper proposes two novel schemes of wideband compressive spectrum sensing (CSS) via block orthogonal matching pursuit (BOMP) algorithm, for achieving high sensing accuracy in real time. These schemes aim to reliably recover the…
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…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…