Abstract. We provide an analytical study of the components of the true signal reconstruction error vs the number of rows of random projection matrix. It is shown that with increasing dimension of the random projector, the deterministic error component decreases and the stochastic one increases. The expressions for calculating the interval of noise levels to ensure the availability of the global minimum error are obtained. The analytical results are confirmed by numerical experiments.

Keywords: discrete ill-posed problem, regularization, random projection, error component, minimum error.