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We study imaging with an array of sensors that probes a medium with single frequency electromagnetic waves and records the scattered electric field. The medium is known and homogenous except for some small and penetrable inclusions. The…

In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…

In this paper, we study the problem of transient signal analysis. A signal-dependent algorithm is proposed which sequentially identifies the countable sets of decay rates and expansion coefficients present in a given signal. We…

Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of…

In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…

Deep Learning has impacted various fields especially in bio-medical applications. Deep learning algorithms work well with both structured and unstructured data. Especially, convolutional neural network work well with signal-based data like…

Functional principal component analysis (FPCA) is a key tool in the study of functional data, driving both exploratory analyses and feature construction for use in formal modeling and testing procedures. However, existing methods for FPCA…

Global and national efforts to deliver high-quality nuclear data to users have a broad impact across applications such as national security, reactor operation, basic science, medical fields, and more. Cross section evaluation is a large…

Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…

Dynamic range limitations in signal processing often lead to clipping, or saturation, in signals. The task of audio declipping is estimating the original audio signal, given its clipped measurements, and has attracted much interest in…

We study the classical simulability of noisy random quantum circuits under general noise models. While various classical algorithms for simulating noisy random circuits have been proposed, many of them rely on the anticoncentration…

Emerging sonography techniques often require increasing the number of transducer elements involved in the imaging process. Consequently, larger amounts of data must be acquired and processed. The significant growth in the amounts of data…

Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…

We consider the problem of estimating an unknown coordinate-wise monotone function given noisy measurements, known as the isotonic regression problem. Often, only a small subset of the features affects the output. This motivates the sparse…

Energy dispersive X-ray (EDX) spectrum imaging yields compositional information with a spatial resolution down to the atomic level. However, experimental limitations often produce extremely sparse and noisy EDX spectra. Under such…

The characterization of multicomponent signals with a particular emphasis on musical and communication signals is one of the problems studied in the dissertation. In order to provide an efficient analysis of the multicomponent signals, the…

Spectral estimation is a fundamental task in signal processing. Recent algorithms in quantum phase estimation are concerned with the large noise, large frequency regime of the spectral estimation problem. The recent work in…

This note proposes a new algorithm for estimating spectral function from limited noisy Matsubara data. We consider both the molecule and condensed matter cases. In each case, the algorithm constructs an interpolant of the Matsubara data and…

In this paper a signal denoising scheme based on Empirical mode decomposition (EMD) is presented. The denoising method is a fully data driven approach. Noisy signal is decomposed adaptively into intrinsic oscillatory components called…

In many scientific applications, measured time series are corrupted by noise or distortions. Traditional denoising techniques often fail to recover the signal of interest, particularly when the signal-to-noise ratio is low or when certain…