Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems

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Reconstructing continuous signals based on a small number of discrete samples is a fundamental problem across science and engineering. We are often interested in signals with "simple" Fourier structure - e.g., those involving frequencies within a bounded r ...

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A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

We propose a novel method of constructing exact Hilbert transform (HT) pairs of wavelet bases using fractional B-splines and state necessary and sufficient conditions for generating such wavelet pairs. In particular, we demonstrate how HT pairs of biorthog ...

In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-hyperboloid

H_+^2

. First, we define a class of suitable dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO ...

Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems

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B-Spline-Based Exact Discretization of Continuous-Domain Inverse Problems With Generalized TV Regularization

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Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

Continuous Wavelet Transform on the Hyperboloid