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Theoretical inverse problems are often studied in an ideal infinite-dimensional setting. The well-posedness theory provides a unique reconstruction of the parameter function, when an infinite amount of data is given. Through the lens of…
Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to…
The compressed sensing (CS) theory has been successfully applied to image compression in the past few years as most image signals are sparse in a certain domain. Several CS reconstruction models have been recently proposed and obtained…
The problem of real-time remote tracking and reconstruction of a two-state Markov process is considered here. A transmitter sends samples from an observed information source to a remote monitor over an unreliable wireless channel. The…
A data set sampled from a certain population is biased if the subgroups of the population are sampled at proportions that are significantly different from their underlying proportions. Training machine learning models on biased data sets…
Reducing acquisition time is a crucial challenge for many imaging techniques. Compressed Sensing (CS) theory offers an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse…
Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
We propose a generalized sampling framework for stochastic graph signals. Stochastic graph signals are characterized by graph wide sense stationarity (GWSS) which is an extension of wide sense stationarity (WSS) for standard time-domain…
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…
This paper builds theoretical foundations for the recovery of a newly proposed class of smooth graph signals, approximately bandlimited graph signals, under three sampling strategies: uniform sampling, experimentally designed sampling and…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
Recent advances in optical systems make them ideal for undersampling multiband signals that have high bandwidths. In this paper we propose a new scheme for reconstructing multiband sparse signals using a small number of sampling channels.…
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…
State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…
Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…
Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted…
This paper considers efficient sampling of simultaneously sparse and correlated (S$\&$C) signals. Such signals arise in various applications in array processing. We propose an implementable sampling architecture for the acquisition of…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
The problem of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy is addressed. Basics of the sampling theory are outlined to show that the lower bound of signal sampling…