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Sparsity is one of the key concepts that allows the recovery of signals that are subsampled at a rate significantly lower than required by the Nyquist-Shannon sampling theorem. Our proposed framework uses arbitrary multiscale transforms,…
The hard thresholding technique plays a vital role in the development of algorithms for sparse signal recovery. By merging this technique and heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent…
Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…
Adaptive thresholding methods have proved to yield high SNRs and fast convergence in finding the solution to the Compressed Sensing (CS) problems. Recently, it was observed that the robustness of a class of iterative sparse recovery…
This thesis consists of original contributions in the area of digital signal processing. The reconstruction of signals sparse (highly concentrated) in various transform domains is the primary problem analyzed in the thesis. The considered…
Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity"…
The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…
This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal…
Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
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…
Compressive sensing relies on the sparse prior imposed on the signal of interest to solve the ill-posed recovery problem in an under-determined linear system. The objective function used to enforce the sparse prior information should be…
Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…
The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.…
We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic…
In this note, we analyze an iterative soft / hard thresholding algorithm with homotopy continuation for recovering a sparse signal $x^\dag$ from noisy data of a noise level $\epsilon$. Under suitable regularity and sparsity conditions, we…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
Motivated by the well-known Papoulis-Gerchberg algorithm, an iterative thresholding algorithm for recovery of sparse signals from few observations is proposed. The sequence of iterates turns out to be similar to that of the thresholded…