Multiscale Modeling and Simulation · 2008 · 458 citations · 42 references
ComputingComputer ScienceBiomedical ImagingComputer VisionDigital ImagingData CompressionDigital Image ProcessingDimensionality ReductionImage ReconstructionImage RestorationRepresentation LearningDictionary LearningImage RepresentationMultiscale Image RepresentationQuadtree DecompositionSingular Value DecompositionSparse CodingSparse LearningSparse Signal Processing
Sparse dictionary learning for grayscale images, exemplified by the K‑SVD algorithm and solved via OMP and SVD, has been a foundational approach in image processing. The authors aim to develop a multiscale sparse representation framework for color images and video using overcomplete dictionaries and quadtree‑based dictionary decomposition. The framework learns overcomplete dictionaries and applies a quadtree decomposition with overlapping patches to construct multiscale sparse representations. The method achieves state‑of‑the‑art performance in various image and video enhancement and restoration tasks, outperforming traditional wavelet dictionaries. Reference: Signal Process., 54 (2006), pp.
This paper presents a framework for learning multiscale sparse representations of color images and video with overcomplete dictionaries. A single-scale K-SVD algorithm was introduced in [M. Aharon, M. Elad, and A. M. Bruckstein, IEEE Trans. Signal Process., 54 (2006), pp. 4311–4322], formulating sparse dictionary learning for grayscale image representation as an optimization problem, efficiently solved via orthogonal matching pursuit (OMP) and singular value decomposition (SVD). Following this work, we propose a multiscale learned representation, obtained by using an efficient quadtree decomposition of the learned dictionary and overlapping image patches. The proposed framework provides an alternative to predefined dictionaries such as wavelets and is shown to lead to state-of-the-art results in a number of image and video enhancement and restoration applications. This paper describes the proposed framework and accompanies it by numerous examples demonstrating its strength.
42