Progressive constrained energy minimization for subpixel detection

Constrained energy minimization (CEM) has been widely used for subpixel detection. It makes use of the sample correlation matrix R by suppressing the background thus enhancing detection of targets of interest. In many real world problems, implementing target detection on a timely basis is crucial, specifically moving targets. However, since the calculation of the sample correlation matrix R needs the complete data set prior to its use in detection, CEM is prevented from being implemented as a real time processing algorithm. In order to resolve this dilemma, the sample correlation matrix R must be replaced with a causal sample correlation matrix formed by only those data samples that have been visited and the currently being processed data sample. This causality is a pre-requisite to real time processing. By virtue of such causality, designing and developing a real time processing version of CEM becomes feasible. This paper presents a progressive CEM (PCEM) where the causal sample correlation matrix can be updated sample by sample. Accordingly, PCEM allows the CEM to be implemented as a causal CEM (C-CEM) as well as real time (RT) CEM via a recursive update equation in real time.