Reconstruction of sparse wavelet signals from partial Fourier measurements

TL;DR

This paper demonstrates that high-dimensional sparse wavelet signals can be reconstructed from a limited set of Fourier measurements, using a deterministic sampling strategy proportional to the signal's sparsity.

Contribution

It introduces a method for reconstructing sparse wavelet signals from partial Fourier data with a deterministic sampling set, expanding the understanding of signal recovery.

Findings

Reconstruction possible with sampling set proportional to sparsity

Deterministic sampling set enables accurate recovery

Applicable to high-dimensional wavelet signals

Abstract

In this paper, we show that high-dimensional sparse wavelet signals of finite levels can be constructed from their partial Fourier measurements on a deterministic sampling set with cardinality about a multiple of signal sparsity.