Data adaptive multi-scale representations for image analysis

Julia Dobrosotskaya; Weihong Guo

doi:10.1117/12.2529695

9 September 2019 Data adaptive multi-scale representations for image analysis

Julia Dobrosotskaya, Weihong Guo

Proceedings Volume 11138, Wavelets and Sparsity XVIII; 1113807 (2019) https://doi.org/10.1117/12.2529695
Event: SPIE Optical Engineering + Applications, 2019, San Diego, California, United States

Abstract

Data adaptive tight frame methods have been proven a powerful sparse approximation tool in a variety of settings. We introduce a model of a data adaptive representation that also provides a multi-scale structure. Our idea is to design a multi-scale frame representation for a given data set, with scaling properties similar to the ones of a wavelet basis, but without the necessary self-similar structure. The adaptivity provides better sparsity properties, using Besov-like norm structure both induces sparsity and helps in identifying important features. We focus on investigating the efficiency of a weighted l¹ constraint in the context of sparse recovery from noisy data and compare it to the weighted l⁰ model alongside. Numerical experiments confirm that the recovered frame vectors assigned lower weights correspond to image elements of larger scale and lower local variation, thus indicating that weighted sparsity in natural images leads to a natural scale separation.

Citation Download Citation

Julia Dobrosotskaya and Weihong Guo "Data adaptive multi-scale representations for image analysis", Proc. SPIE 11138, Wavelets and Sparsity XVIII, 1113807 (9 September 2019); https://doi.org/10.1117/12.2529695

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