Compressive Sensing of Sparse Signals in the Hermite Transform Basis: Analysis and Algorithm for Signal Reconstruction
Milo\v{s} Brajovic, Irena Orovic, Milos Dakovic, Srdjan Stankovic
TL;DR
This paper analyzes how missing samples affect sparse signals in the Hermite transform domain and proposes a non-iterative reconstruction algorithm based on probabilistic detection thresholds.
Contribution
It introduces a probabilistic analysis of Hermite coefficients for undersampled signals and develops a simple, non-iterative compressive sensing reconstruction algorithm.
Findings
Success probability for component detection is quantified.
A detection threshold is derived from statistical properties.
The algorithm is validated through multiple examples.
Abstract
An analysis of the influence of missing samples in signals exhibiting sparsity in the Hermite transform domain is provided. Based on the statistical properties derived for the Hermite coefficients of randomly undersampled signal, the probability of success in detection of signal components support is determined. Based on the probabilistic analysis, a threshold for the detection of signal components is provided. It is a crucial step in the definition of a simple non-iterative algorithm for compressive sensing signal reconstruction. The derived theoretical concepts are proved on several examples using different statistical tests.
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Image and Signal Denoising Methods · Mathematical Analysis and Transform Methods