Related papers: Constrained Sampling: Optimum Reconstruction in Su…

The problem of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy is addressed. Basics of the sampling theory are outlined to show that the lower bound of signal sampling…

This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective…

Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…

We present a new algorithm based on posterior sampling for learning in Constrained Markov Decision Processes (CMDP) in the infinite-horizon undiscounted setting. The algorithm achieves near-optimal regret bounds while being advantageous…

Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with…

Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…

Compressed sensing (CS) MRI relies on adequate undersampling of the k-space to accelerate the acquisition without compromising image quality. Consequently, the design of optimal sampling patterns for these k-space coefficients has received…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

We study the problem of reconstructing a signal from its projection on a subspace. The proposed signal reconstruction algorithms utilize a guiding subspace that represents desired properties of reconstructed signals. We show that optimal…

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…

In clinical trials and other applications, we often see regions of the feature space that appear to exhibit interesting behaviour, but it is unclear whether these observed phenomena are reflected at the population level. Focusing on a…

We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…

We study a class of real robust phase retrieval problems under a Gaussian assumption on the coding matrix when the received signal is sparsely corrupted by noise. The goal is to establish conditions on the sparsity under which the input…

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…

Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…

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.…

In this paper, we study the compressed sensing reconstruction problem with generalized elastic net prior (GENP), where a sparse signal is sampled via a noisy underdetermined linear observation system, and an additional initial estimation of…

Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…

Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…

We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…