Total Variation Wavelet Inpainting
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Constrained and SNR-Based Solutions for TV-Hilbert Space Image Denoising
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A comparison of three total variation based texture extraction models
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Sparse approximation of images inspired from the functional architecture of the primary visual areas
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Image inpainting by patch propagation using patch sparsity
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Multidimensional Systems and Signal Processing
Compression and denoising using l0-norm
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Journal of Mathematical Imaging and Vision
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Journal of Scientific Computing
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Journal of Scientific Computing
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GREC'11 Proceedings of the 9th international conference on Graphics Recognition: new trends and challenges
Simultaneous image fusion and super-resolution using sparse representation
Information Fusion
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The separation of image content into semantic parts plays a vital role in applications such as compression, enhancement, restoration, and more. In recent years, several pioneering works suggested such a separation be based on variational formulation and others using independent component analysis and sparsity. This paper presents a novel method for separating images into texture and piecewise smooth (cartoon) parts, exploiting both the variational and the sparsity mechanisms. The method combines the basis pursuit denoising (BPDN) algorithm and the total-variation (TV) regularization scheme. The basic idea presented in this paper is the use of two appropriate dictionaries, one for the representation of textures and the other for the natural scene parts assumed to be piecewise smooth. Both dictionaries are chosen such that they lead to sparse representations over one type of image-content (either texture or piecewise smooth). The use of the BPDN with the two amalgamed dictionaries leads to the desired separation, along with noise removal as a by-product. As the need to choose proper dictionaries is generally hard, a TV regularization is employed to better direct the separation process and reduce ringing artifacts. We present a highly efficient numerical scheme to solve the combined optimization problem posed by our model and to show several experimental results that validate the algorithm's performance.