Sparse Representation for Color Image Restoration

By Julien Mairal, Michael Elad, Guillermo Sapiro. 2008

1,856 citations recorded by the source corpus.

Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted dictionaries for images has been a major challenge. The K-SVD has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks. In this paper, we address the problem of learning dictionaries for color images and extend the K-SVD-based grayscale image denoising algorithm that appears in . This work puts forward ways for handling nonhomogeneous noise and missing information, paving the way to state-of-the-art results in applications such as color image denoising, demosaicing, and inpainting, as demonstrated in this paper.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Media Technology

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Citations in the corpus

Semantic Image Inpainting with Deep Generative Models (2016, neutral): “Unlike previous hand-crafted matching and editing, learning based methods have shown promising results [27, 38, 33, 22].”
Online Learning for Matrix Factorization and Sparse Coding (2009, methodology): “For instance, using ℓ′′ has proven experimentally to be particularly well adapted to image denoising (Elad and Aharon, 2006; Mairal et al., 2008b).”
Mask-Specific Inpainting with Deep Neural Networks (2014, methodology): “We used input patches of size 39 × 39 pixels, whereas [14] used a dictionary with patch size 9 × 9 pixels.”
Sparse Representation Based Fisher Discrimination Dictionary Learning for Image Classification (2014, methodology): “(16) can be efficiently solved by updating each dictionary atom one by one via the algorithm like (Yang et al. 2010c) or (Mairal et al. 2008c).”
Multiresolution Bilateral Filtering for Image Denoising (2008, neutral): “[10]–[12] develop gray-scale and color image denoising algorithms based on sparse and redundant representations over learned dictionaries , where training and denoising use the K-SVD algorithm; [13] and [14] group 2-”
Spike and Slab Variational Inference for Multi-Task and Multiple Kernel Learning (2011, result): “Similar experiments in other datasets have confirmed the above remarks.”
Simultaneous image fusion and denoising with adaptive sparse representation (2015, background): “For each image patch x , the error tolerance in (1) is adaptively set as 1 = (cid:1)(cid:1) n √ C s [30] to calculate the sparse vector α where C > 0 is a constant.”
Convolutional Sparse Coding for Image Super-Resolution (2015, background): “By far, sparse representation has achieved state-of-the-art results in various computer vision tasks [15, 24, 30].”
From Heuristic Optimization to Dictionary Learning: A Review and Comprehensive Comparison of Image Denoising Algorithms (2014, methodology): “In the past decade, it has been successfully applied to denoising problems [29], [42], [71].”
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images (2009, background): “Due to space imitations, we are unable to discuss many other interesting examples, including problems in array processing [114, 115], inpainting in images [68, 88, 89, 72], image decomposition to cartoon and texture [122, 148, 147], and others [99, 7, 113, 137].”
Learning Deep CNN Denoiser Prior for Image Restoration (2017, methodology): “However, existing methods mainly focus on modeling gray image prior and there are only a few works concentrating on modeling color image prior (see, e.g ., [16, 41, 46]).”
Pixel-level image fusion with simultaneous orthogonal matching pursuit (2012, background): “Applications that benefit from the sparsity and overcompleteness include compression, regularization in inverse problems [29], image and video compression [30,31], computer vision tasks and so on [32].”
Semantic Image Inpainting with Perceptual and Contextual Losses (2016, background): “Unlike the previous hand-crafted matching and editing, sparse coding is proposed to recover the images from a learned dictionary [18].”
Sparse Representation for Target Detection in Hyperspectral Imagery (2011, background): “We will also investigate the design and exploitation of more discriminative dictionaries learned from the training data [37], [40].”