Exploiting Structure in Wavelet-Based Bayesian Compressive Sensing

By Lihan He, Lawrence Carin. IEEE Transactions on Signal Processing, 2009

527 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/3cee8fa1fa72fa60e458f35e724254d5498889f0

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In Computational Mechanics

In Computer Vision and Pattern Recognition

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Citations in the corpus

ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing (2017, background): “statistical dependencies [18, 51], structure [13], etc.”
Structured Sparse Principal Component Analysis (2009, background): “Recent research on structured sparsity has highlighted the ben fit of exploiting such structure in the context of regression and classification [3, 4, 5], compress ed ensing [6], as well as within Bayesian frameworks [7].”
Learning with structured sparsity (2009, background): “He et al. recently extend the idea to the tree sparsity in the Bayesian framework [11, 12].”
ADMM-CSNet: A Deep Learning Approach for Image Compressive Sensing (2020, methodology): “Initially, sparse regularization was exploited in an image domain or a conventional transform domain [11], [12], [13], such as gradient or wavelet domain.”
Group Lasso with Overlaps: the Latent Group Lasso approach (2011, unknown): “Keywords: group Lasso, sparsity, graph, support recovery, block regularization, feature selection”
Bayesian Compressive Sensing Via Belief Propagation (2008, methodology): “Consequently, it is possible to decode signals from fewer measurements using an algorithm that allocates different distributions to different coefficients [38, 48].”
WIRE: Wavelet Implicit Neural Representations (2023, background): “Wavelets typically result in faster approximation rates for signals and images than Fourier transform [15], and hence they are often used for image compression [16, 40] and as a robust prior for inverse problems of images [18] and videos [48].”
Proximal Methods for Hierarchical Sparse Coding (2010, unknown): “…decompositions lend themselves well to this tree organization because of their multiscale structure, and beneﬁt from it for image compression and denoising (Shapiro, 1993; Crouse et al., 1998; Baraniuk, 1999; Baraniuk et al., 2002, 2010; He and Carin, 2009; Zhao et al., 2009; Huang et al., 2009).”
Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images (2011, methodology): “dictionaries as discussed here or based upon more traditional expansions (DCT or wavelets) and newer CS inversion methods [2], [19].”
Off-Grid Direction of Arrival Estimation Using Sparse Bayesian Inference (2011, background): “One merit of SBI is its ﬂexibility in modeling sparse signals that can not only promote the sparsity of its solution, e.g., in [11], but also exploit the possible structure of the signal to be recovered, e.g., in [14].”