Abstract Suppose we wish to recover a vector x 0 ∈ ℝ 𝓂 (e.g., digital signal or image) from incomplete and contaminated observations y = A + e ; is an 𝓃 × matrix with far fewer rows than columns (𝓃 ≪ 𝓂) error term. Is it possible accurately based on the data ? To , consider solution # 𝓁 1 ‐regularization problem where ϵ size of term . We show that if obeys uniform uncertainty principle (with unit‐normed columns) sufficiently sparse, then within noise level As first example, suppose Gaussian...

Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The tree (HMT) model captures the key features of joint probability density wavelet coefficients real-world data. One potential drawback HMT framework is need computationally expensive iterative training fit an a given data set (e.g., using expectation-maximization algorithm). We greatly simplify by exploiting inherent self-similarity images. simplified specifies parameters with...

Low-rank matrices play a fundamental role in modeling and computational methods for signal processing machine learning. In many applications where low-rank arise, these cannot be fully sampled or directly observed, one encounters the problem of recovering matrix given only incomplete indirect observations. This paper provides an overview modern techniques exploiting structure to perform recovery settings, providing survey recent advances this rapidly-developing field. Specific attention is...

We consider the problem of recovering two unknown vectors, w and x, length L from their circular convolution. make structural assumption that vectors are members known subspaces, one with dimension N other K. Although observed convolution is nonlinear in both it linear rank-1 matrix formed by outer product wx*. This observation allows us to recast deconvolution as low-rank recovery measurements, whose natural convex relaxation a nuclear norm minimization program. prove effectiveness this...

Abstract Spatial resolution, spectral contrast and occlusion are three major bottlenecks for non-invasive inspection of complex samples with current imaging technologies. We exploit the sub-picosecond time resolution along provided by terahertz time-domain spectroscopy to computationally extract occluding content from layers whose thicknesses wavelength comparable. The method uses statistics reflected electric field at subwavelength gaps lock into each layer position then a time-gated...

The theory of compressive sensing enables accurate and robust signal reconstruction from a number measurements dictated by the signal's structure rather than its Fourier bandwidth. A key element is role played randomization. In particular, signals that are compressible in time or space domain can be recovered just few randomly chosen coefficients. However, some scenarios we only observe magnitude coefficients not their phase. this paper, study magnitude-only problem parallel with existing...

Most of the existing sparse-recovery methods assume a static system: signal is finite-length vector for which fixed set measurements and sparse representation are available an l1 problem solved reconstruction. However, same reconstruction framework not readily applicable in streaming changes over time, it measured reconstructed sequentially small intervals. This particularly desired when dividing signals into disjoint blocks processing each block separately infeasible or inefficient. In this...

We introduce and analyze a new technique for model reduction deep neural networks. While large networks are theoretically capable of learning arbitrarily complex models, overfitting redundancy negatively affects the prediction accuracy variance. Our Net-Trim algorithm prunes (sparsifies) trained network layer-wise, removing connections at each layer by solving convex optimization program. This program seeks sparse set weights that keeps inputs outputs consistent with originally model. The...

To recover a sparse signal from an underdetermined system, we often solve constrained <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\ell _{1}$</tex></formula> -norm minimization problem. In many cases, the sparsity and recovery performance can be further improved by replacing norm with "weighted" norm. Without prior information about signal's nonzero elements, procedure for selecting weights is...

In this paper we present a complete (hardware/ software) sub-Nyquist rate (× 13) wideband signal acquisition chain capable of acquiring radar pulse parameters in an instantaneous bandwidth spanning 100 MHz-2.5 GHz with the equivalent 8 effective number bits (ENOB) digitizing performance. The approach is based on alternative sensing-paradigm compressed sensing (CS). hardware platform features fully-integrated CS receiver architecture named random-modulation preintegrator (RMPI) fabricated...

The COVID-19 pandemic has created many challenges that need immediate attention. Various epidemiological and deep learning models have been developed to predict the outbreak, but all limitations affect accuracy robustness of predictions. Our method aims at addressing these making earlier more accurate outbreak predictions by (1) using patients' EHR data from different counties states encode local disease status medical resource utilization condition; (2) considering demographic similarity...

In this work we address the problem of state estimation in dynamical systems using recent developments compressive sensing and sparse approximation. We formulate traditional Kalman filter as a one-step update optimization procedure which leads us to more unified framework, useful for incorporating sparsity constraints. introduce three combinations two conditions (sparsity innovations) write recursive programs estimate each model. This paper is meant an overview different methods into dynamic...

We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating vector from dictionary using just few non-zero coefficients). This class plays significant role in both theories coding and applications signal processing. However, LCA lacks its convergence properties previous results on networks for nonsmooth optimization do not apply to specifics architecture. show has desirable...

We propose a flexible convex relaxation for the phase retrieval problem that operates in natural domain of signal. Therefore, we avoid prohibitive computational cost associated with "lifting" and semidefinite programming (SDP) methods such as PhaseLift compete recently developed non-convex techniques retrieval. relax quadratic equations phaseless measurements to inequality constraints each which representing symmetric "slab". Through simple program, our proposed estimator finds an extreme...

We study distributed optimization problems over a network when the communication between nodes is constrained, and therefore, information that exchanged must be quantized. Recent advances using gradient algorithm with quantization scheme at fixed resolution have established convergence, but rates significantly slower than communications are unquantized. In this article, we introduce novel method, which refer to as adaptive quantization, allows us match convergence under perfect...

Multiresolution signal and image models such as the hidden Markov tree aim to capture statistical structure of smooth singular (edgy) regions. Unfortunately, based on orthogonal wavelet transform suffer from shift-variance, making them less accurate realistic. We extend HMT modeling framework complex transform, which features near shift-invariance improved angular resolution compared standard transform. The model is computationally efficient (with linear-time computation processing...

The wavelet transform provides a sparse representation for smooth images, enabling efficient approximation and compression using techniques such as zerotrees. Unfortunately, this sparsity does not extend to piecewise where edge discontinuities separating regions persist along contours. This lack of hampers the efficiency wavelet-based compression. On class images containing C2 separated by edges contours, example, asymptotic rate-distortion (R-D) performance zerotree-based coding is limited...

Source localization by matched-field processing (MFP) generally involves solving a number of computationally intensive partial differential equations. This paper introduces technique that mitigates this computational workload “compressing” these computations. Drawing on key concepts from the recently developed field compressed sensing, it shows how low-dimensional proxy for Green’s function can be constructed backpropagating small set random receiver vectors. Then source located performing...

We study gradient methods for solving distributed convex optimization problems over a network when the communication bandwidth between nodes is limited, and so information that exchanged must be quantized. This imperfect poses fundamental challenge, if not properly accounted may prevent convergence of these algorithms. Our first contribution in this article to propose modified consensus-based method such using random (dithered) quantization. algorithm can interpreted as variant...

We present a general architecture for the acquisition of ensembles correlated signals. The signals are multiplexed onto single line by mixing each one against different code and then adding them together, resulting signal is sampled at high rate. show that if M signals, band limited to W/2 Hz, can be approximated superposition R <; underlying ensemble recovered sampling rate within logarithmic factor RW, as compared with cumulative Nyquist MW. This theorem shows correlation structure...

We study the policy evaluation problem in multi-agent reinforcement learning. In this problem, a group of agents works cooperatively to evaluate value function for global discounted accumulative reward which is composed local rewards observed by agents. Over series time steps, act, get rewarded, update their estimate function, then communicate with neighbors. The at each agent can be interpreted as distributed consensus-based variant popular temporal difference learning algorithm TD(0)....