Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images

By Mingyuan Zhou, Haojun Chen, John William Paisley, Lu Ren, Lingbo Li, Zhengming Xing, David B. Dunson, Guillermo Sapiro, Lawrence Carin. IEEE Transactions on Image Processing, 2011

390 citations recorded by the source corpus.

Nonparametric Bayesian methods are considered for recovery of imagery based upon compressive, incomplete, and/or noisy measurements. A truncated beta-Bernoulli process is employed to infer an appropriate dictionary for the data under test and also for image recovery. In the context of compressive sensing, significant improvements in image recovery are manifested using learned dictionaries, relative to using standard orthonormal image expansions. The compressive-measurement projections are also optimized for the learned dictionary. Additionally, we consider simpler (incomplete) measurements, defined by measuring a subset of image pixels, uniformly selected at random. Spatial interrelationships within imagery are exploited through use of the Dirichlet and probit stick-breaking processes. Several example results are presented, with comparisons to other methods in the literature.

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

View Paper: https://www.semanticscholar.org/paper/5f735197f2834c021d18f4c4d22aa703ed1a63d2

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Citations in the corpus

Nonlocal Image Restoration With Bilateral Variance Estimation: A Low-Rank Approach (2013, background): “Bayesian compressed sensing [22], [23]) observations and 81”
Missing Information Reconstruction of Remote Sensing Data: A Technical Review (2015, neutral): “, the aforementioned spectral-based methods [18], [77], [78] and temporal-based methods [58], [59], [79].”
Solving Inverse Problems With Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity (2010, methodology): “In the recent non-parametric Baye si n approach [71], an image patch clustering is implemented with probability models, which improves the de noising and inpainting results, although still under performing, in quality and computational cost, the fr amework here introduced.”
Beta-Negative Binomial Process and Poisson Factor Analysis (2011, background): “It has diverse applications including document classiﬁcation (Thibaux and Jordan, 2007), dictionary learning (Zhou et al., 2012, 2009, 2011) and topic modeling (Li et al., 2011).”
Sparse Representation Based Fisher Discrimination Dictionary Learning for Image Classification (2014, background): “Instead, learning the desired dictionaries from the training data with sparsity regularization has led to state-of-the-art results in image reconstruction (Elad and Aharon 2006; Bryt and Elad 2008; Aharon et al. 2006; Mairal et al. 2012; Zhou et al. 2012) and image classification (Mairal et al.”
Image Denoising Using the Higher Order Singular Value Decomposition (2013, positive): “Recently, other successful denoising techniques, such as [46] and [41] (which use Gaussian mixture models) or [19], [44], and [45] (which learn overcomplete dictionaries), have emerged.”
A Deep Generative Deconvolutional Image Model (2015, background): “(Mairal et al., 2008; Zhang and Li, 2010; Zhou et al., 2012) based on a set of image patches .”
A Survey of Sparse Representation: Algorithms and Applications (2015, methodology): “[131] developed a nonparametric Bayesian dictionary learning algorithm, which utilized hi erarchical Bayesian to model parameters and employed the truncated beta-Bernoulli process to learn the dictionary.”