The statistical properties analysis of reconstruction error in greedy pursuit algorithms: Taking OMP as an example

Greedy pursuit algorithms are widely used in sparse signal processing for their computational efficiency. However, research on the reconstruction error properties is far from comprehensive. This paper derives the statistical properties of reconstruction error in greedy pursuit algorithms, including probability density function (PDF), expectation, and covariance. The reconstruction error follows a mixture distribution, which is composed of multiple multivariate random variables and weighted by the probability of support sets. The multivariate random variable obeys a truncated distribution that results from restricting the noise domain. The validity of the derivations is verified by using the orthogonal matching pursuit (OMP) algorithm as an example. This paper delves into the statistical properties of the reconstruction error in greedy pursuit algorithms. It establishes that the reconstruction error follows a mixture multivariate truncated Gaussian distribution. The OMP algorithm is taken as an example to derive the PDF, expectation, and covariance matrix of the reconstruction error.