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Wavelet Variants for 2D Analysis

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Digital Signal Processing with Matlab Examples, Volume 2

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Abstract

This chapter is devoted to the analysis of 2D signals and/or images, with emphasis on the use of wavelet variants. Many important applications are interested on such methods. In particular, the detection of edges, borders, contours, etc., is suitable for several purposes, like for instance spatially selective filtering (for example, in medical studies that want to have a clearer view of vessels against a noisy image background). By using wavelets, simple methods can be devised for image denoising and compression. The first sections of the chapter focus on how to obtain wavelet decompositions of images. It is noticed that the decomposition would be better if it was adapted to characteristics of the image, to take into account–for instance-certain predominant directions or curves. The central sections of the chapter introduce wavelet versions, like ridgelets, curvelets, contourlets, bandelets, etc. that try to capture these characteristics. The final sections contains experiments about image denoising, and pointers to the literature on applications.

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Giron-Sierra, J.M. (2017). Wavelet Variants for 2D Analysis. In: Digital Signal Processing with Matlab Examples, Volume 2. Signals and Communication Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-2537-2_4

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