Phase retrieval for wavelet transforms

Phase retrieval for the Cauchy wavelet transform

We consider the phase retrieval problem in which one tries to reconstruct a function from the modulus of its wavelet transform. We study the unicity and stability of the reconstruction. In the case where the wavelets are Cauchy wavelets, we prove that the modulus of the wavelet transform uniquely determines the function up to a global phase. We show that the reconstruction operator is continuou...

Classical Wavelet Transforms over Finite Fields

This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...

Fixing of Cycle Slips in Dual-Frequency GPS Phase Observables using Discrete Wavelet Transforms

The occurrence of cycle slips is a major limiting factor for achievement of sub-decimeter accuracy in positioning with GPS (Global Positioning System). In the past, several authors introduced a method based on different combinations of GPS data together with Kalman filter to solve the problem of the cycle slips. In this paper the same philosophy is used but with discrete wavelet transforms. For...

Stabilized wavelet transforms for non -

Wavelet Transforms for Nonlinear Signal

Robert Nowak Michigan State University East Lansing, MI 48824-1226 Email: [email protected] WWW: http://www.egr.msu.edu/spc/ Richard Baraniuk Rice University Houston, TX 77251-1892 Email: [email protected] WWW:http://www-dsp.rice.edu ABSTRACT In this paper we describe two new structures for nonlinear signal processing. The new structures simplify the analysis, design, and implementation of nonlin...