Related papers: Restricted Conformal Property of Compressive Sensi…
Inspired by significant real-life applications, in particular, sparse phase retrieval and sparse pulsation frequency detection in Asteroseismology, we investigate a general framework for compressed sensing, where the measurements are…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
The study of the restricted isometry property (RIP) of corrupted random matrices is particularly important in the field of compressed sensing (CS) with corruptions. If a matrix still satisfies the RIP after that a certain portion of rows…
In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search…
The existence and uniqueness conditions are a prerequisite for reliable reconstruction of sparse signals from reduced sets of measurements within the Compressive Sensing (CS) paradigm. However, despite their underpinning role for practical…
Conformal prediction (CP) quantifies the uncertainty of machine learning models by constructing sets of plausible outputs. These sets are constructed by leveraging a so-called conformity score, a quantity computed using the input point of…
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…
We consider compressive sensing as a source coding method for signal transmission. We concatenate a convolutional coding system with 1-bit compressive sensing to obtain a serial concatenated system model for sparse signal transmission over…
For any black-box model, conformal prediction (CP) returns prediction sets guaranteed to include the true label with high adjustable probability. Robust CP (RCP) extends the guarantee to the worst case noise up to a pre-defined magnitude.…
Compressive sensing (CS) is a promising technology for realizing energy-efficient wireless sensors for long-term health monitoring. In this paper, we propose a data-driven CS framework that learns signal characteristics and individual…
The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
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…
Spectrum resources management of growing demands is a challenging problem and Cognitive Radio (CR) known to be capable of improving the spectrum utilization. Recently, Power Spectral Density (PSD) map is defined to enable the CR to reuse…
Can compression algorithms be employed for recovering signals from their underdetermined set of linear measurements? Addressing this question is the first step towards applying compression algorithms for compressed sensing (CS). In this…
This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…
We consider reflector imaging in a weakly random waveguide. We address the situation in which the source is farther from the reflector to be imaged than the energy equipartition distance, but the receiver array is closer to the reflector to…
Structures play a significant role in the field of signal processing. As a representative of structural data, low rank matrix along with its restricted isometry property (RIP) has been an important research topic in compressive signal…
Compressive sensing has been receiving a great deal of interest from researchers in many areas because of its ability in speeding up data acquisition. This framework allows fast signal acquisition and compression when signals are sparse in…
The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose…