Iterative Preconditioned Steepest Descent Reconstruction using Blob-Based Basis Functions

Abstract

Using iterative algorithms, such as the steepest descent for image restoration or reconstruction can sometimes suffer from low convergence rate. By preconditioning the algorithms, one can increase the convergence rate. However, the iterative preconditioned algorithms can be further improved by replacing pixels with blobs as the basis functions for reconstruction. In this paper, using the blob-based basis functions in the iterative preconditioned steepest descent algorithm for single image reconstruction or super-resolution reconstruction, we obtain even better results with lower reconstruction errors. We also show that the blob-based iterative algorithm can stabilize the reconstruction error such that it stays at its minimum at higher number of iterations.