Restoration and Super-Resolution of Diffraction-Limited Imagery Data by Bayesian and Set-Theoretic Approaches

Abstract

Abstract : This project was primarily aimed at the design of novel algorithms for the restoration and super-resolution processing of imagery data to improve the resolution in images acquired from practical sensing operations. Due to the underlying diffraction limits, the image recorded at the output of the imaging system is usually a low-pass filtered version of the original scene and hence recovery of the lost information contributing to the finer details is required to produce resolution enhancement. Super-resolution algorithms attempt to provide not only passband restoration but also some degree of spectral extrapolation thus enabling to restore the high frequency spatial amplitude variations relating to the spatial resolution of the sensor and lost due to diffraction-limited imaging. These algorithms are typically iterative in nature and implement nonlinear signal processing operations. Two distinct approaches that have resulted in powerful super-resolution algorithms are based on statistical optimization arguments and set-theoretic estimation procedures. The principal objectives in this project were to develop and evaluate specific techniques for developing new processing algorithms by combining the strong points of the two approaches. The principal outcomes from this work include the following: (1) Systematic procedures for extracting and modeling scene-derived information sets for projection-based set- theoretic super-resolution processing; and (2) Design of hybrid processing algorithms that integrate Projection Onto Convex Sets (POCS) iterations with Maximum Likelihood (ML) estimation procedures to yield superior restoration and super-resolution performance.