On Round-Off Errors and Gaussian Blur in Superresolution and in Image Registration

TL;DR

This paper investigates the impact of round-off errors and Gaussian blur on superresolution and image registration, proposing methods to accurately align and segment signals despite these challenges.

Contribution

It introduces a signal-dependent measurement model and demonstrates conditions under which discontinuities can be correctly identified using dynamic programming.

Findings

Successful alignment and segmentation under certain blur and noise conditions

Theoretical proof of correct discontinuity detection with dynamic programming

Analysis of the effects of round-off errors on superresolution accuracy

Abstract

Superresolution theory and techniques seek to recover signals from samples in the presence of blur and noise. Discrete image registration can be an approach to fuse information from different sets of samples of the same signal. Quantization errors in the spatial domain are inherent to digital images. We consider superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions which are subject to blur which is Gaussian or a mixture of Gaussians as well as to round-off errors. We describe a signal-dependent measurement matrix which captures both types of effects. For this setting we show that the difficulties in determining the discontinuity points from two sets of samples even in the absence of other types of noise. If the samples are also subject to statistical noise, then it is necessary to align and segment the data sequences to make the most effective inferences about the amplitudes and discontinuity points. Under some conditions on the blur, the noise, and the distance between discontinuity points, we prove that we can correctly align and determine the first samples following each discontinuity point in two data sequences with an approach based on dynamic programming.