Related papers: Dequantizing Compressed Sensing: When Oversampling…
We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…
This paper addresses optimal decoding strategies in lossy compression where the assumed distribution for compressor design mismatches the actual (true) distribution of the source. This problem has immediate relevance in standardized…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this…
We consider the Linear Programming (LP) solution of the Compressed Sensing (CS) problem over reals, also known as the Basis Pursuit (BasP) algorithm. The BasP allows interpretation as a channel-coding problem, and it guarantees error-free…
Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often…
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…
Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
Representing a continuous-time signal by a set of samples is a classical problem in signal processing. We study this problem under the additional constraint that the samples are quantized or compressed in a lossy manner under a limited…
Parallel acquisition systems arise in various applications in order to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating…
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…
In the problem of compressive phase retrieval, one wants to recover an approximately $k$-sparse signal $x \in \mathbb{C}^n$, given the magnitudes of the entries of $\Phi x$, where $\Phi \in \mathbb{C}^{m \times n}$. This problem has…
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…
This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the $\ell^1$-synthesis basis pursuit allows for a simultaneous…
Incorporating diffusion models in the image compression domain has the potential to produce realistic and detailed reconstructions, especially at extremely low bitrates. Previous methods focus on using diffusion models as expressive…
Image denoising aims to remove noise while preserving structural details and perceptual realism, yet distortion-driven methods often produce over-smoothed reconstructions, especially under strong noise and distribution shift. This paper…
We develop a Bayesian framework for sensing which adapts the sensing time and/or basis functions to the instantaneous sensing quality measured in terms of the expected posterior mean-squared error. For sparse Gaussian sources a significant…