Multiscale methods for the segmentation and reconstruction of signals and images

This paper addresses the problem of both segmenting and reconstructing a no isy signal or image. The work is motivated by Image problems arising in cer tain scientific applications, such as medical imaging. Two objectives for a segmentation and denoising algorithm are laid out: it should be computatio nally efficient and capable of generating statistics for the errors in the reconstruction and estimates of the boundary locations. The starting point for the development of a suitable algorithm is a variational approach to se gmentation [1]. This paper then develops a precise statistical interpretati on of a one-dimensional (1-D) version of this variational approach to segme ntation. The 1-D algorithm that arises as a result of this analysis is comp utationally efficient and capable of generating error statistics. A straigh tforward extension of this algorithm to two dimensions would incorporate re cursive procedures for computing estimates df inhomogeneous Gaussian Markov random fields. Such procedures require an unacceptably large number of ope rations. To meet the objective of developing a computationally efficient al gorithm, the use of recently developed multiscale statistical methods is in vestigated. This results in the development of an algorithm for segmenting and denoising which is not only computationally efficient but also capable of generating error statistics, as desired.