Parametric estimation in noisy blind deconvolution model: a new estimation procedure

TL;DR

This paper introduces a new estimation method for inverse filters and noise levels in a complex noisy blind deconvolution model, leveraging Hankel form properties, with proven consistency and empirical validation.

Contribution

It presents a novel estimation procedure specifically designed for noisy blind deconvolution models, including distribution estimation and theoretical properties.

Findings

Estimates are strongly consistent.

Asymptotic distribution of estimates is derived.

Simulation confirms good computational performance.

Abstract

In a parametric framework, the paper is devoted to the study of a new estimation procedure for the inverse filter and the level noise in a complex noisy blind discrete deconvolution model. Our estimation method is a consequence of the sharp exploitation of the specifical properties of the Hankel forms. The distribution of the input signal is also estimated. The strong consistency and the asymptotic distribution of all estimates are established. A consistent simulation study is added in order to demonstrate empirically the computational performance of our estimation procedures.