Super-Resolution Reconstruction of Image Sequences

ÐIn an earlier work, we have introduced the problem of reconstructing a super-resolution image sequence from a given low resolution sequence. We proposed two iterative algorithms, the R-SD and the R-LMS, to generate the desired image sequence. These algorithms assume the knowledge of the blur, the down-sampling, the sequences motion, and the measurements noise characteristics, and apply a sequential reconstruction process. It has been shown that the computational complexity of these two algorithms makes both of them practically applicable. In this paper, we rederive these algorithms as approximations of the Kalman filter and then carry out a thorough analysis of their performance. For each algorithm, we calculate a bound on its deviation from the Kalman filter performance. We also show that the propagated information matrix within the R-SD algorithm remains sparse in time, thus ensuring the applicability of this algorithm. To support these analytical results we present some computer simulations on synthetic sequences, which also show the computational feasibility of these algorithms. Index TermsÐImage restoration, super resolution, dynamic estimation, kalman filter, adaptive filters, recursive least squares (RLS), least mean squares (LMS), steepest descent (SD).