2024/12/12 by Serap A. Savari, Savari, Serap A.
Computer Science · Engineering · #Image and Signal Denoising Methods #Advanced Image Processing Techniques #Advanced Image Fusion Techniques
paper · pdf · doi:10.48550/arxiv.2412.09741
Superresolution theory and techniques seek to recover signals from samples in\nthe presence of blur and noise. Discrete image registration can be an approach\nto fuse information from different sets of samples of the same signal.\nQuantization errors in the spatial domain are inherent to digital images. We\nconsider superresolution and discrete image registration for one-dimensional\nspatially-limited piecewise constant functions which are subject to blur which\nis Gaussian or a mixture of Gaussians as well as to round-off errors. We\ndescribe a signal-dependent measurement matrix which captures both types of\neffects. For this setting we show that the difficulties in determining the\ndiscontinuity points from two sets of samples even in the absence of other\ntypes of noise. If the samples are also subject to statistical noise, then it\nis necessary to align and segment the data sequences to make the most effective\ninferences about the amplitudes and discontinuity points. Under some conditions\non the blur, the noise, and the distance between discontinuity points, we prove\nthat we can correctly align and determine the first samples following each\ndiscontinuity point in two data sequences with an approach based on dynamic\nprogramming.\n