Martin Vetterli

TL;DR: A "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information is pursued and it is shown that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves.

TL;DR: A simple, nonrigorous, synthetic view of wavelet theory is presented for both review and tutorial purposes, which includes nonstationary signal analysis, scale versus frequency,Wavelet analysis and synthesis, scalograms, wavelet frames and orthonormal bases, the discrete-time case, and applications of wavelets in signal processing.

TL;DR: An adaptive, data-driven threshold for image denoising via wavelet soft-thresholding derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution widely used in image processing applications.

TL;DR: Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding and developed the theory in both continuous and discrete time.

TL;DR: The perfect reconstruction condition is posed as a Bezout identity, and it is shown how it is possible to find all higher-degree complementary filters based on an analogy with the theory of Diophantine equations.