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Compressive Sensing (CS) is a new paradigm for the efficient acquisition of signals that have sparse representation in a certain domain. Traditionally, CS has provided numerous methods for signal recovery over an orthonormal basis. However,…

Information Theory · Computer Science 2019-05-08 Jianchen Zhu , Shengjie Zhao , Qingjiang Shi , Gonzalo R. Arce

This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…

Machine Learning · Statistics 2025-04-15 The Tien Mai

This paper investigates the sparse optimal allocation of sensors for detecting sparse leaking emission sources. Because of the non-negativity of emission rates, uncertainty associated with parameters in the forward model, and sparsity of…

Applications · Statistics 2025-09-09 Xinchao Liu , Youngdeok Hwang , Dzung Phan , Levente Klein , Xiao Liu , Kyongmin Yeo

We study a multiple measurement vector (MMV) approach to synthetic aperture radar (SAR) imaging of scenes with direction dependent reflectivity and with polarization diverse measurements. The data are gathered by a moving transmit- receive…

Optimization and Control · Mathematics 2017-11-08 Liliana Borcea , Ilker Kocyigit

We present a compressive radar design that combines multitone linear frequency modulated (LFM) waveforms in the transmitter with a classical stretch processor and sub-Nyquist sampling in the receiver. The proposed compressive illumination…

Information Theory · Computer Science 2022-04-13 Nithin Sugavanam , Siddharth Baskar , Emre Ertin

As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random…

Information Theory · Computer Science 2016-07-22 Shan Huang , Hong Sun , Haijian Zhang , Lei Yu

Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…

Functional Analysis · Mathematics 2025-04-02 Giovanni S. Alberti , Alessandro Felisi , Matteo Santacesaria , S. Ivan Trapasso

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…

Numerical Analysis · Mathematics 2023-03-07 Jan Glaubitz , Anne Gelb , Guohui Song

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to…

Data Analysis, Statistics and Probability · Physics 2011-01-19 Nicolas Dobigeon , Alfred O. Hero , Jean-Yves Tourneret

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…

Numerical Analysis · Mathematics 2020-11-17 Ana Carpio , Sergei Iakunin , Georg Stadler

The recent theory of compressive sensing leverages upon the structure of signals to acquire them with much fewer measurements than was previously thought necessary, and certainly well below the traditional Nyquist-Shannon sampling rate.…

This paper proposes to leverage intelligent reflecting surface (IRS) backscatter to realize radio-frequency-chain-free uplink-transmissions (RFCF-UT). In this communication paradigm, IRS works as an information carrier, whose elements are…

Signal Processing · Electrical Eng. & Systems 2022-07-22 Sai Xu , Yanan Du , Jiliang Zhang , Jiangzhou Wang , Jie Zhang

This paper presents a variational based approach to fusing hyperspectral and multispectral images. The fusion process is formulated as an inverse problem whose solution is the target image assumed to live in a much lower dimensional…

Computer Vision and Pattern Recognition · Computer Science 2023-07-19 Qi Wei , José Bioucas-Dias , Nicolas Dobigeon , Jean-Yves Tourneret

In this paper, we present a Bayesian channel estimation algorithm for multicarrier receivers based on pilot symbol observations. The inherent sparse nature of wireless multipath channels is exploited by modeling the prior distribution of…

Machine Learning · Statistics 2013-03-07 Niels Lovmand Pedersen , Carles Navarro Manchón Bernard Henri Fleury

Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS…

Computer Vision and Pattern Recognition · Computer Science 2017-08-29 Duc Minh Nguyen , Evaggelia Tsiligianni , Nikos Deligiannis

Fourier ptychography (FP) is a powerful light-based synthetic aperture imaging technique that allows one to reconstruct a high-resolution, wide field-of-view image by computationally integrating a diverse collection of low-resolution,…

Image and Video Processing · Electrical Eng. & Systems 2025-07-21 Matthew A. Chan , Casey J. Pellizzari , Christopher A. Metzler

We introduce the sparse direct sampling method (DSM) to estimate properties of a region from signals that probe the region. We demonstrate the sparse-DSM on two separate problems: estimating both the angle-of-arrival of a radio wave…

Analysis of PDEs · Mathematics 2020-10-19 Isaac Harris , Jacob D Rezac

Imaging objects with high relative permittivity and large electrical size remains a challenging problem in the field of inverse scattering. In this work we present a phaseless inverse scattering method that can accurately image and…

Applied Physics · Physics 2021-10-08 Amartansh Dubey , Samruddhi Deshmukh , Li Pan , Xudong Chen , Ross Murch

We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The…

Information Theory · Computer Science 2015-05-27 Yoav Shechtman , Yonina C. Eldar , Alexander Szameit , Mordechai Segev

This paper aims at developing a clustering approach with spectral images directly from CASSI compressive measurements. The proposed clustering method first assumes that compressed measurements lie in the union of multiple low-dimensional…

Image and Video Processing · Electrical Eng. & Systems 2019-11-06 Jianchen Zhu , Tong Zhang , Shengjie Zhao , Carlos Hinojosa , Zengli Liu , Gonzalo R. Arce
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