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We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…

Information Theory · Computer Science 2012-02-13 Mahdi Cheraghchi

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 this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…

Machine Learning · Computer Science 2016-10-18 Lijun Zhang , Tianbao Yang , Rong Jin , Zhi-Hua Zhou

Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…

Machine Learning · Statistics 2026-05-13 Jin Zhu , Junxian Zhu , Zezhi Wang , Borui Tang , Hongmei Lin , Xueqin Wang

We identify and overcome two key obstacles in extending the success of BERT-style pre-training, or the masked image modeling, to convolutional networks (convnets): (i) convolution operation cannot handle irregular, random-masked input…

Computer Vision and Pattern Recognition · Computer Science 2023-01-11 Keyu Tian , Yi Jiang , Qishuai Diao , Chen Lin , Liwei Wang , Zehuan Yuan

In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…

Image and Video Processing · Electrical Eng. & Systems 2019-09-17 Joseph Daws , Armenak Petrosyan , Hoang Tran , Clayton G. Webster

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

Numerical Analysis · Computer Science 2009-01-08 Wei Dai , Olgica Milenkovic

Compressed sensing (CS) has emerged to overcome the inefficiency of Nyquist sampling. However, traditional optimization-based reconstruction is slow and can not yield an exact image in practice. Deep learning-based reconstruction has been a…

Image and Video Processing · Electrical Eng. & Systems 2024-09-20 Seongmin Hong , Jaehyeok Bae , Jongho Lee , Se Young Chun

3D scene reconstruction from 2D images has been a long-standing task. Instead of estimating per-frame depth maps and fusing them in 3D, recent research leverages the neural implicit surface as a unified representation for 3D reconstruction.…

Computer Vision and Pattern Recognition · Computer Science 2023-09-19 Xinyi Yu , Liqin Lu , Jintao Rong , Guangkai Xu , Linlin Ou

The sparse-driven radar imaging can obtain the high-resolution images about target scene with the down-sampled data. However, the huge computational complexity of the classical sparse recovery method for the particular situation seriously…

Quantum Physics · Physics 2022-01-05 Xiaowen Liu , Chen Dong , Ying Luo , Le Kang , Yong Liu , Qun Zhang

In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting…

Machine Learning · Statistics 2015-05-28 Hojjat S. Mousavi , Vishal Monga , Trac D. Tran

In this note, we consider a special instance of the scaled, inexact and adaptive generalised Fast Iterative Soft-Thresholding Algorithm (SAGE-FISTA) recently proposed in (Rebegoldi, Calatroni, '21) for the efficient solution of strongly…

Optimization and Control · Mathematics 2021-04-02 Luca Calatroni , Simone Rebegoldi

We propose a new mass-mapping algorithm, specifically designed to recover small-scale information from a combination of gravitational shear and flexion. Including flexion allows us to supplement the shear on small scales in order to…

Cosmology and Nongalactic Astrophysics · Physics 2016-06-08 Francois Lanusse , Jean-Luc Starck , Adrienne Leonard , Sandrine Pires

In recent years, point cloud perception tasks have been garnering increasing attention. This paper presents the first attempt to estimate 3D human body mesh from sparse LiDAR point clouds. We found that the major challenge in estimating…

Computer Vision and Pattern Recognition · Computer Science 2025-10-03 Bohao Fan , Wenzhao Zheng , Jianjiang Feng , Jie Zhou

We consider algorithms and recovery guarantees for the analysis sparse model in which the signal is sparse with respect to a highly coherent frame. We consider the use of a monotone version of the fast iterative shrinkage- thresholding…

Optimization and Control · Mathematics 2015-06-17 Zhao Tan , Yonina C. Eldar , Amir Beck , Arye Nehorai

Images acquired with a telescope are blurred and corrupted by noise. The blurring is usually modeled by a convolution with the Point Spread Function and the noise by Additive Gaussian Noise. Recovering the observed image is an ill-posed…

Instrumentation and Methods for Astrophysics · Physics 2021-11-03 Fadi Nammour , Morgan A. Schmitz , Fred Maurice Ngolè Mboula , Jean-Luc Starck , Julien N. Girard

In this paper, we propose the family of Iterative Methods with Adaptive Thresholding (IMAT) for sparsity promoting reconstruction of Delta Modulated (DM) voice signals. We suggest a novel missing sampling approach to delta modulation that…

Information Theory · Computer Science 2020-02-11 Mahdi Boloursaz Mashhadi , Saber Malekmohammadi , Farokh Marvasti

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

Reconstructing hand-held objects in 3D from monocular images remains a significant challenge in computer vision. Most existing approaches rely on implicit 3D representations, which produce overly smooth reconstructions and are…

Computer Vision and Pattern Recognition · Computer Science 2025-07-22 Zerui Chen , Rolandos Alexandros Potamias , Shizhe Chen , Cordelia Schmid

We propose and analyze a solution to the problem of recovering a block sparse signal with sparse blocks from linear measurements. Such problems naturally emerge inter alia in the context of mobile communication, in order to meet the…

Information Theory · Computer Science 2020-09-23 Ingo Roth , Martin Kliesch , Axel Flinth , Gerhard Wunder , Jens Eisert