Related papers: A Class of Deterministic Sensing Matrices and Thei…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
In this paper, we consider compressive sensing (CS)-based recovery of delays and Doppler frequencies of targets in high resolution radars. We propose a novel sub-Nyquist sampling method in the Fourier domain based on difference sets (DS),…
Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is…
In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as measurement matrix. The samples are subsequently forwarded to…
We explain theoretically a curious empirical phenomenon: "Approximating a matrix by deterministically selecting a subset of its columns with the corresponding largest leverage scores results in a good low-rank matrix surrogate". To obtain…
In traditional compressed sensing theory, the dictionary matrix is given a priori, whereas in real applications this matrix suffers from random noise and fluctuations. In this paper we consider a signal model where each column in the…
Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for…
Linear encoding of sparse vectors is widely popular, but is commonly data-independent -- missing any possible extra (but a priori unknown) structure beyond sparsity. In this paper we present a new method to learn linear encoders that adapt…
The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…
In this paper we deal with the linear frequency modulated signals and radar signals that are affected by disturbance which is the inevitable phenomenon in everyday communications. The considered cases represent the cases when the signals of…
We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter…
We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured matrix (a randomly sub-sampled circulant matrix) and is robust to analog pre-quantization noise…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a…
In phase retrieval problems, a signal of interest (SOI) is reconstructed based on the magnitude of a linear transformation of the SOI observed with additive noise. The linear transform is typically referred to as a measurement matrix. Many…
Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon,…
As compared to using randomly generated sensing matrices, optimizing the sensing matrix w.r.t. a carefully designed criterion is known to lead to better quality signal recovery given a set of compressive measurements. In this paper, we…
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…
In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…