Tuesday, February 18, 2020 | 2:30PM | Yost 306

Title: Exact Evaluation of the Triple Integral Products of Wavelet Functions and Applications in Inverse Problems

Abstract

After a brief introduction into wavelets with compact support that generate orthonormal bases in $L^2$, I will prove a theorem that triple and higher integral products of the functions from an orthonormal wavelet basis can be computed precisely, without numerical integration, as the solutions of a well posed system of linear equations.

This allows to rewrite relationships involving quotients and products of functions in the wavelet domain in a new form beneficial for certain inverse problems.  I will discuss applications of this approach to parameter recovery of PDE solutions from  undersampled data and  to deconvolution of non-smooth signals. I will also formulate partial results and numerically supported conjectures about the recovery of functions that are jointly sparse in a wavelet basis from their  quotient.