Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images

Zhou, Mingyuan; Chen, Haojun; Paisley, John; Ren, Lu; Li, Lingbo; Xing, Zhengming; Dunson, David B.; Sapiro, Guillermo; Carin, Lawrence

doi:10.1109/tip.2011.2160072

Cited by 314 publications

(37 citation statements)

References 36 publications

(86 reference statements)

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“…The beta-Bernoulli process provides a convenient prior for the sparse coefficients [20][21][22][23]. The process meaning distribution over distribution is a combination of a Beta distribution and a Bernoulli one.…”

Section: Sparse Prior Factormentioning

confidence: 99%

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Restoring Aqua MODIS band 6 by other spectral bands using compressed sensing theory

Shen

Zeng

et al. 2012

2012 4th Workshop on Hyperspectral Image and Signal Processing (WHISPERS)

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The Aqua satellite launched in May 2002 is a key one in the Earth Observation System (EOS) mission of NASA. In the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor aboard the Aqua, 15 of all the 20 detectors in the band 6 are out of working. Therewith missing data exists. It is very significant to find the way to reconstruct its incomplete data efficiently. This paper proposes an approach to retrieve the missing data by the newborn Compressed Sensing (CS) theory, which can account for not only the large-area inpainting, but also the spatial autocorrelation property and the complementarity relationship among spectral bands. The experimental results validate that the proposed algorithm performs well compared with the state of-art methods.

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Section: Sparse Prior Factormentioning

confidence: 99%

“…The impact of the parameters above on the model are expatiated in [23], without restatementation here. Note that the product signation n means that each component of Z i and Jr is drawn from i. i. d (independently identically distributed).…”

Section: Sparse Prior Factormentioning

confidence: 99%

Restoring Aqua MODIS band 6 by other spectral bands using compressed sensing theory

Shen

Zeng

et al. 2012

2012 4th Workshop on Hyperspectral Image and Signal Processing (WHISPERS)

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“…Image restoration is an important and widely studied subject in image processing, where the main objective is to reconstruct the latent image given the degraded and/or noisy image [1][2][3][4][5]. The main detrimental factors to corrupt the image are noise, data missing, and blur, to name a few.…”

Section: Introductionmentioning

confidence: 99%

Image Recovery with Data Missing in the Presence of Salt-and-Pepper Noise

et al. 2019

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In this paper, an image recovery problem under the case of salt-and-pepper noise and data missing that degrade image quality is addressed if they are not effectively handled, where the salt-and-pepper noise as the impulsive noise is remodeled as a sparse signal due to its impulsiveness and the data missing pattern, denoted by a sparse vector, contains only zeros and ones to formulate the data missing. In particular, the salt-and-pepper noise and data missing are reformatted by their sparsity, respectively. The wavelet and framelet domains are explored to sparsely represent the image in order to accurately reconstruct the clean image. From the reformulations conducted and to recover the image, under one optimization framework, a joint estimation is developed to perform the image recovery, the salt-and-pepper noise suppression, and the missing patter estimation. To solve the optimization problem, two efficient solvers are developed to obtain the joint estimation solution, and they are based on the alternating direction method of multipliers (ADMM) and accelerated proximal gradient (APG). Finally, numerical studies verify that the joint estimation algorithm outperforms the state-of-the-art approaches in terms of both objective and subjective evaluation standards.

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“…Two patches are viewed the same or called rotationally invariant, if they are the same up to rotation. While the patch space model and diffusion-based algorithms have been successfully applied to different fields, such as the inpainting problem [22][23][24][25] and the medical imaging problem [19,26,27], however, to the best of our knowledge, a companion theoretical study is lacking. It is not clear how we could correctly find the neighbors when noise exists, and why the patch size should be neither too big nor too small and thus why patch space approaches are better than pixel-based ones.…”

Section: Introductionmentioning

confidence: 99%

Manifold Learning via the Principle Bundle Approach

Lin

Minasian

et al. 2018

Front. Appl. Math. Stat.

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In this paper, we propose a novel principal bundle model and apply it to the image denoising problem. This model is based on the fact that the patch manifold admits canonical groups actions such as rotation. We introduce an image denoising algorithm, called the diffusive vector non-local Euclidean median (dvNLEM), by combining the traditional nonlocal Euclidean median (NLEM), the rotational structure in the patch space, and the diffusion distance. A theoretical analysis of dvNLEM, as well as the traditional nonlocal Euclidean median (NLEM), is provided to explain why these algorithms work. In particular, we show how accurate we could obtain the true neighbors associated with the rotationally invariant distance (RID) and Euclidean distance in the patch space when noise exists, and how we could apply the diffusion geometry to stabilize the selected metric. The dvNLEM is applied to an image database of 1,361 images and a comparison with the NLEM is provided. Different image quality assessments based on the error-sensitivity or the human visual system are applied to evaluate the performance.

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Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images

Cited by 314 publications

References 36 publications

Restoring Aqua MODIS band 6 by other spectral bands using compressed sensing theory

Restoring Aqua MODIS band 6 by other spectral bands using compressed sensing theory

Image Recovery with Data Missing in the Presence of Salt-and-Pepper Noise

Manifold Learning via the Principle Bundle Approach

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