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We develop a Recursive $\mathcal{L}_1$-Regularized Least Squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight…
This work investigates the problem of signal recovery from undersampled noisy sub-Gaussian measurements under the assumption of a synthesis-based sparsity model. Solving the $\ell^1$-synthesis basis pursuit allows for a simultaneous…
Recent developments in Carrillo et al. (2012) and Carrillo et al. (2013) introduced a novel regularization method for compressive imaging in the context of compressed sensing with coherent redundant dictionaries. The approach relies on the…
Classical total variation (TV) based iterative reconstruction algorithms assume that the signal is piecewise smooth, which causes reconstruction results to suffer from the over-smoothing effect. To address this problem, this work presents a…
We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted $\ell_{2,1}$ ($\mathit{ow}\ell_{2,1}$), which is specifically designed to take…
We present a method for supervised learning of sparsity-promoting regularizers for image denoising. Sparsity-promoting regularization is a key ingredient in solving modern image reconstruction problems; however, the operators underlying…
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…
In this paper, we propose a new sparse signal recovery algorithm, referred to as sparse Kalman tree search (sKTS), that provides a robust reconstruction of the sparse vector when the sequence of correlated observation vectors are available.…
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…
The Compressive Sensing (CS) as a novel acquisition approach that finds its usage in image processing. The hypothesis like this one assures signal recovery with high quality from decreased number of samples compared with the number required…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
Conventional compressed sensing theory assumes signals have sparse representations in a known, finite dictionary. Nevertheless, in many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the…
Classical model reduction techniques project the governing equations onto a linear subspace of the original state space. More recent data-driven techniques use neural networks to enable nonlinear projections. Whilst those often enable…
Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
Image super-resolution (SR) is one of the long-standing and active topics in image processing community. A large body of works for image super resolution formulate the problem with Bayesian modeling techniques and then obtain its…
We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is…
Sparse learning has been widely studied to capture critical information from enormous data sources in the filed of system identification. Often, it is essential to understand internal working mechanisms of unknown systems (e.g. biological…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…