Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising-part II: adaptive algorithms

• Published in: IEEE transactions on image processing Vol. 15; no. 3; pp. 555 - 571
• Main Author: Guleryuz, O.G.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive algorithm; Adaptive algorithms; Algorithm design and analysis; Algorithms; Applied sciences; Approximation algorithms; Artificial Intelligence; Computer Graphics; Computer Simulation; Data models; Detection, estimation, filtering, equalization, prediction; Engineering profession; Error concealment; Estimates; Exact sciences and technology; Image edge detection; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image reconstruction; image recovery; Image segmentation; Imaging, Three-Dimensional - methods; Information Storage and Retrieval - methods; Information, signal and communications theory; inpainting; iterated denoising; Miscellaneous; Models, Statistical; Noise reduction; nonlinear approximation; Nonlinear Dynamics; Nonlinearity; Pattern recognition; Pattern Recognition, Automated - methods; Progressions; Reproducibility of Results; Sensitivity and Specificity; Signal and communications theory; Signal processing; Signal Processing, Computer-Assisted; Signal, noise; sparse recovery; sparse representations; Studies; Telecommunications and information theory; Texture; Transforms; image recovery; Adaptive algorithm; Segmentation; Image processing; Predictor; Noise reduction; Error concealment; sparse representations; Iterative method; Shape detection; Adaptive method; Texture; Image reconstruction; inpainting; Sparse representation; nonlinear approximation; sparse recovery; Missing data; Simulation; Linear transformation; Signal processing; Feature extraction; iterated denoising; Error correction; Edge detection; Preconditioning
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2005.863055

We combine the main ideas introduced in Part I with adaptive techniques to arrive at a powerful algorithm that estimates missing data in nonstationary signals. The proposed approach operates automatically based on a chosen 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. Unlike prevalent algorithms, our method does not necessitate any complex preconditioning, segmentation, or edge detection steps, and it can be written as a progression of denoising operations. We show that constructing estimates based on nonlinear approximants is fundamentally a nonconvex problem and we propose a progressive algorithm that is designed to deal with this issue directly. The algorithm is applied to images through an extensive set of simulation examples, primarily on missing regions containing textures, edges, and other image features that are not readily handled by established estimation and recovery methods. We discuss the properties required of good transforms, and in conjunction, show the types of regions over which well-known transforms provide good predictors. We further discuss extensions of the algorithm where the utilized transforms are also chosen adaptively, where unpredictable signal components in the progressions are identified and not predicted, and where the prediction scenario is more general.