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Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…

Computation · Statistics 2026-03-04 Radhika Kulkarni , Brani Vidakovic

Autoencoders are a prominent model in many empirical branches of machine learning and lossy data compression. However, basic theoretical questions remain unanswered even in a shallow two-layer setting. In particular, to what degree does a…

Machine Learning · Computer Science 2024-02-08 Kevin Kögler , Alexander Shevchenko , Hamed Hassani , Marco Mondelli

The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…

Information Theory · Computer Science 2014-08-27 Peter Jung , Philipp Walk

It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…

Methodology · Statistics 2007-11-13 Emmanuel J. Candes , Michael B. Wakin , Stephen P. Boyd

In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…

Information Theory · Computer Science 2015-06-18 Jun Fang , Jing Li , Yanning Shen , Hongbin Li , Shaoqian Li

Volumetric image compression has become an urgent task to effectively transmit and store images produced in biological research and clinical practice. At present, the most commonly used volumetric image compression methods are based on…

Image and Video Processing · Electrical Eng. & Systems 2022-10-19 Dongmei Xue , Haichuan Ma , Li Li , Dong Liu , Zhiwei Xiong

This short note studies a variation of the Compressed Sensing paradigm introduced recently by Vaswani et al., i.e. the recovery of sparse signals from a certain number of linear measurements when the signal support is partially known. The…

Information Theory · Computer Science 2010-02-21 Laurent Jacques

Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…

Statistical Mechanics · Physics 2012-06-07 Florent Krzakala , Marc Mézard , François Sausset , Yifan Sun , Lenka Zdeborová

Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…

Information Theory · Computer Science 2010-10-04 Nam Yul Yu

The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…

Optics · Physics 2009-09-15 Albert C. Fannjiang

This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and…

Functional Analysis · Mathematics 2014-07-08 Bogdan Roman , Anders Hansen , Ben Adcock

Image deblurring is a classical computer vision problem that aims to recover a sharp image from a blurred image. To solve this problem, existing methods apply the Encode-Decode architecture to design the complex networks to make a good…

Image and Video Processing · Electrical Eng. & Systems 2021-10-13 Wenbin Zou , Mingchao Jiang , Yunchen Zhang , Liang Chen , Zhiyong Lu , Yi Wu

We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. We introduce an $\ell_2$ regularized formulation of CS which we…

Signal Processing · Electrical Eng. & Systems 2024-07-15 Dimitris Bertsimas , Nicholas A. G. Johnson

Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically…

Optics · Physics 2020-11-17 Maria Bancerek , Krzysztof M. Czajkowski , Rafal Kotynski

This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…

Information Theory · Computer Science 2013-02-12 Xiaofu Wu , Zhen Yang , Lu Gan

In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…

Computer Vision and Pattern Recognition · Computer Science 2013-11-25 Will Landecker , Rick Chartrand , Simon DeDeo

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key…

Applications · Statistics 2009-11-13 François-Xavier Dupé , Jalal Fadili , Jean Luc Starck

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

We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (i.e.…

Image and Video Processing · Electrical Eng. & Systems 2024-06-28 Gaurav Arya , William F. Li , Charles Roques-Carmes , Marin Soljačić , Steven G. Johnson , Zin Lin

In this letter we study the subwavelength imaging of sparse broadband sources inside a disordered medium by processing the data acquired by a single antenna. A mathematical model has been developed for solving such problem based on the idea…

Optics · Physics 2015-06-18 Lianlin Li , Fang Li , Tie Jun Cui