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The recently proposed modified-compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on…
We propose a new iterative greedy algorithm for reconstructions of sparse signals with or without noisy perturbations in compressed sensing. The proposed algorithm, called \emph{subspace thresholding pursuit} (STP) in this paper, is a…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
The Computational Singular Perturbation (CSP) method of Lam and Goussis is an iterative method to reduce the dimensionality of systems of ordinary differential equations with multiple time scales. In [J. Nonlin. Sci., to appear], the…
Compressive sensing (CS) is a new technology which allows the acquisition of signals directly in compressed form, using far fewer measurements than traditional theory dictates. Recently, many so-called signal space methods have been…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…
Compressed Sensing (CS) is an appealing framework for applications such as Magnetic Resonance Imaging (MRI). However, up-to-date, the sensing schemes suggested by CS theories are made of random isolated measurements, which are usually…
This paper proposes a DC microgrid state estimation and sensor placement method based on compressive sensing. Formulations of various types of measurements and components are developed under the proposed framework. A measurement placing…
Learning stabilizing controllers from data is an important task in engineering applications; however, collecting informative data is challenging because unstable systems often lead to rapidly growing or erratic trajectories. In this work,…
Compressed sensing (CS) is an important theory for sub-Nyquist sampling and recovery of compressible data. Recently, it has been extended by Pham and Venkatesh to cope with the case where corruption to the CS data is modeled as impulsive…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
In compressed sensing (CS) framework, a signal is sampled below Nyquist rate, and the acquired compressed samples are generally random in nature. However, for efficient estimation of the actual signal, the sensing matrix must preserve the…
Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises…
Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS…
This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…
This note proposes a data-driven output-feedback stabilizing policy iteration for unknown linear discrete-time systems with unmeasurable states. Existing policy iteration methods for optimal control must start from a stabilizing control…
We consider the problem of in-network compressed sensing from distributed measurements. Every agent has a set of measurements of a signal $x$, and the objective is for the agents to recover $x$ from their collective measurements using only…
The reconstruction of sparse signals from a limited set of measurements poses a significant challenge as it necessitates a solution to an underdetermined system of linear equations. Compressed sensing (CS) deals with sparse signal…