Millimeter-wave (mmWave) communication systems rely on large-scale antenna arrays to combat large path-loss at mmWave band. Due hardware characteristics and deployment environments, are vulnerable element blockages failures, which necessitate diagnostic techniques locate faulty elements for calibration purposes. Current require full or partial knowledge of channel state information (CSI), can b...

Sparsity is a very powerful prior for the identification of signals from noisy indirect measurements. The recovery of the signal is usually performed by suitable linearly constrained optimizations with additional sparsity enforcing barriers. Depending on the specific formulation, one can produce a variety of different algorithms. In this Chapter the numerical realizations of such linear and non...

When using `1 minimization to recover a sparse, nonnegative solution to a underdetermined linear system of equations, what is the highest sparsity level at which recovery can still be guaranteed? Recently, Donoho and Tanner [10] discovered, by invoking classic results from the theory of convex polytopes [11, 12], that the highest sparsity level equals half of the number of equations. In this pa...

One approach to accelerating data acquisition in magnetic resonance imaging is acquisition of partial k-space data and recovery of missing data based on the sparsity of the image in the wavelet transform domain. We hypothesize that the application of stationary wavelet transform (SWT) thresholding as a sparsity-promoting operation results in improved artifact removal performance in comparison w...

In this paper we consider memoryless one-bit compressed sensing with randomly subsampled Gaussian circulant matrices. We show that in a small sparsity regime and for small enough accuracy $\delta$, $m\sim \delta^{-4} s\log(N/s\delta)$ measurements suffice to reconstruct the direction of any $s$-sparse vector up to accuracy $\delta$ via an efficient program. We derive this result by proving that...

Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns. Recently, there were introduced sparsity measures that take into account such joint sparsity patterns, promoting coupling of non-vanishing components. These ...

The problem of recovering complex signals from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in fusion frames, we introduce a framework for splitting the complex information into local pieces. Each piece of information is measured by potentially very low quality senso...

We study a deep linear network expressed under the form of a matrix factorization problem. It takes as input a matrix X obtained by multiplying K matrices (called factors and corresponding to the action of a layer). Each factor is obtained by applying a fixed linear operator to a vector of parameters satisfying a sparsity constraint. In machine learning, the error between the product of the est...

The standard approach to recover a signal with a sparse representation in D is to design a measurement matrix ΦD ∈ Cm×n which allows the recovery of any f ∈ Σk from the measurement vector ΦDf whenever k is sufficiently small. While a minimal requirement for the recovery of any f ∈ Σk is that the constructed map ΦD : Σ D k −→ C, f 7→ ΦDf is injective, the recent literature on sparse signal recov...