Related papers: ICR: Iterative Convex Refinement for Sparse Signal…
Sparse reconstruction approaches using the re-weighted l1-penalty have been shown, both empirically and theoretically, to provide a significant improvement in recovering sparse signals in comparison to the l1-relaxation. However, numerical…
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to…
Passive synthetic aperture radar (SAR) uses existing signals of opportunity such as communication and broadcasting signals. In our prior work, we have developed a low-rank matrix recovery (LRMR) method that can reconstruct scenes with…
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
We derive near optimal performance guarantees for subsampled blind deconvolution. Blind deconvolution is an ill-posed bilinear inverse problem and additional subsampling makes the problem even more challenging. Sparsity and spectral…
The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind…
Compressed sensing is a central topic in signal processing with myriad applications, where the goal is to recover a signal from as few observations as possible. Iterative re-weighting is one of the fundamental tools to achieve this goal.…
Blind single image super-resolution (SISR) is a challenging task in image processing due to the ill-posed nature of the inverse problem. Complex degradations present in real life images make it difficult to solve this problem using na\"ive…
The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…
Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving linear inverse problems is often challenging, with ill-conditioned operators and potentially non-unique solutions. Embedding prior knowledge, such as…
Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have…
We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed…
This paper studies the problem of Kronecker-structured sparse vector recovery from an underdetermined linear system with a Kronecker-structured dictionary. Such a problem arises in many real-world applications such as the sparse channel…
This article considers the challenge of accommodating outlier measurements in state estimation. The Risk-Averse Performance-Specified (RAPS) state estimation approach addresses outliers as a measurement selection Bayesian risk minimization…
We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract phase retrieval), where convex optimization problems are…
Integrated sensing and communication (ISAC) is expected to be offered as a fundamental service in the upcoming sixth-generation (6G) communications standard. However, due to the exposure of information-bearing signals to the sensing…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…