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In this paper, we study the sample complexity and develop efficient optimal algorithms for 1-bit phase retrieval: recovering a signal $\mathbf{x}\in\mathbb{R}^n$ from $m$ phaseless bits…
In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation (QEM) is essential for producing reliable outputs from quantum circuits. We present a statistical signal processing approach to QEM that estimates the most likely…
We consider the reconstruction of a bandlimited function from its finite localized sample data. Truncating the classical Shannon sampling series results in an unsatisfactory convergence rate due to the slow decayness of the sinc function.…
Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
Memoryless scalar quantization (MSQ) is a common technique to quantize frame coefficients of signals (which are used as a model for generalized linear samples), making them compatible with our digital technology. The process of quantization…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…
We investigate the optimal performance of dense sensor networks by studying the joint source-channel coding problem. The overall goal of the sensor network is to take measurements from an underlying random process, code and transmit those…
Monte Carlo simulations of neutronic systems are computationally intensive and demand significant memory resources for high-fidelity modeling. Compressed sensing enables accurate reconstruction of signals from significantly fewer samples…
Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…
The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…
Motivated by the structure reconstruction problem in single-particle cryo-electron microscopy, we consider the multi-target detection model, where multiple copies of a target signal occur at unknown locations in a long measurement, further…
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…
Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental…
We provide a scheme for exploring the reconstruction limit of compressed sensing by minimizing the general cost function under the random measurement constraints for generic correlated signal sources. Our scheme is based on the statistical…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
We study generative compressed sensing when the measurement matrix is randomly subsampled from a unitary matrix (with the DFT as an important special case). It was recently shown that $\textit{O}(kdn\| \boldsymbol{\alpha}\|_{\infty}^{2})$…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…