Introduction: In order to reduce patient setup error in treatment field, portal images with treatment beam (megavoltage x-ray) are widely used. These images are acquired by electronic portal imaging devices (EPID). However, portal images suffer from insufficient anatomical information, contrast, and spatial resolution, because of the fact that Compton scatter is the main photon...

In this paper we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case we have the solution as a multiresolution expansion in the base of compactly supported wavelet basis. The solution is parametrized by the solutions of two reduced algebraical problems, one is nonlinear and the second is some li...

Wavelet decomposition has recently been generalized to binary field in which the arithmetic is performed wholly in GF(2). In order to maintain an invertible binary wavelet transform with desirable multiresolution properties, the bandwidth, the perfect reconstruction and the vanishing moment constraints are placed on the binary filters. While they guarantee an invertible transform, the transform...

Let KMM 󸀠󸀠(R) be the generalized tempered distributions of eeMMMMMM-growth with restricted order rr r N0, where the function MM(MM) grows faster than any linear functions as |MM| x x. We show the convergence of multiresolution expansions ofKMM(R) in the test function spaceKMM(R) ofKMM(R). In addition, we show that the kernel of an integral operatorKK K KMM(R) x KMM(R) provides approximation ord...

New methods for compact image coding based on generalized wavelet decompositions have been introduced recently. Unlike in the classical wavelet decomposition scheme it is possible to use diier-ent scaling and wavelet functions at every scale by using non-stationary multiresolution analyses. In this work we introduce parallel algorithms (suitable for MIMD architectures) that excel the execution ...

In this work, we consider the problem of blind source separation in the wavelet domain via a Bayesian estimation framework. We use the sparsity and multiresolution properties of the wavelet coefficients to model their distribution by heavy tailed prior probability laws: the generalized exponential family and the Gaussian mixture family. Appropriate MCMC algorithms are developped in each case fo...

This survey paper examines the work of J. von Neumann and M.H. Stone as it relates to the abstract theory of wavelets. In particular, we discuss the direct integral theory of von Neumann and how it can be applied to representations of certain discrete groups to study the existence of normalized tight frames in the setting of Gabor systems and wavelets, via the use of group representations and v...

Our work explores the transfer of knowledge at multiple levels of abstraction to improve learning. By exploiting the similarities between objects at various levels of detail, multiresolution learning can facilitate transfer between image classification tasks. We extract features from images at multiple levels of resolution, then use these features to create models at different resolutions. Upon...

Despite being routinely required in medical applications, deformable surface registration is notoriously difficult due to large intersubject variability and complex geometry of most medical datasets. We present a general and flexible deformable matching framework based on generalized surface flows that efficiently tackles these issues through tailored deformation priors and multiresolution comp...