Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
Patch-based video processing: a variational Bayesian approach
IEEE Transactions on Circuits and Systems for Video Technology
Mixture model-and least squares-based packet video error concealment
IEEE Transactions on Image Processing
An iterative Bayesian algorithm for sparse component analysis in presence of noise
IEEE Transactions on Signal Processing
Image restoration through L0 analysis-based sparse optimization in tight frames
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Image inpainting by patch propagation using patch sparsity
IEEE Transactions on Image Processing
A shrinkage learning approach for single image super-resolution with overcomplete representations
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Denoising of medical images using a reconstruction-average mechanism
Digital Signal Processing
Geometrically Guided Exemplar-Based Inpainting
SIAM Journal on Imaging Sciences
Self-content super-resolution for ultra-HD up-sampling
Proceedings of the 9th European Conference on Visual Media Production
On analysis-based two-step interpolation methods for randomly sampled seismic data
Computers & Geosciences
Object removal and loss concealment using neighbor embedding methods
Image Communication
Computationally Efficient Formulation of Sparse Color Image Recovery in the JPEG Compressed Domain
Journal of Mathematical Imaging and Vision
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We study the robust estimation of missing regions in images and video using adaptive, sparse reconstructions. Our primary application is on missing regions of pixels containing textures, edges, and other image features that are not readily handled by prevalent estimation and recovery algorithms. We assume that we are given a linear transform that is expected to provide sparse decompositions over missing regions such that a portion of the transform coefficients over missing regions are zero or close to zero. We adaptively determine these small magnitude coefficients through thresholding, establish sparsity constraints, and estimate missing regions in images using information surrounding these regions. Unlike prevalent algorithms, our approach does not necessitate any complex preconditioning, segmentation, or edge detection steps, and it can be written as a sequence of denoising operations. We show that the region types we can effectively estimate in a mean-squared error sense are those for which the given transform provides a close approximation using sparse nonlinear approximants. We show the nature of the constructed estimators and how these estimators relate to the utilized transform and its sparsity over regions of interest. The developed estimation framework is general, and can readily be applied to other nonstationary signals with a suitable choice of linear transforms. Part I discusses fundamental issues, and Part II is devoted to adaptive algorithms with extensive simulation examples that demonstrate the power of the proposed techniques.