The Optimal Estimates of the Shift Parameter of Images in Orthogonal Function Bases

Abstract

By means of the maximum likelihood method, we carry out synthesis and analysis of the algorithm for estimation of the shift parameter of the one-dimensional image presented as a set of serial expansion coefficients according to the system of orthogonal functions. We consider the possibility of employment of both asynchronous and synchronous orthogonal basis in order to implement the measurer of the image shift parameter. We also show that, in general, the measurer with synchronous basis produces more exact estimate of the shift parameter than the receiver with asynchronous basis, provided the identical number of expansion coefficients (modes) is processed.