Problem statement: Digital images play an important role both in daily life applications as well as in areas of research and technology. Due to the increasing traffic caused by multimedia information and digitized form of representation of images; image compression has become a necessity. Approach: Wavelet transform has demonstrated excellent image compression performance. New algorithms based ...

Lifting is a procedure for deriving strong valid inequalities for a closed set from inequalities that are valid for its lower dimensional restrictions. It is arguably one of the most effective ways of strengthening linear programming relaxations of 0–1 programming problems. Wolsey (1977) and Gu et al. (2000) show that superadditive lifting functions lead to sequence independent lifting of valid...

We consider a class of packing problems with uncertain data, which we refer to as the chance-constrained binary packing problem. In this problem, a subset of items is selected that maximizes the total profit so that a generic packing constraint is satisfied with high probability. Interesting special cases of our problem include chance-constrained knapsack and set packing problems with random co...

This paper presents a new wavelet family for lossless image compression by re-factoring the channel representation of the update-then-predict lifting wavelet, introduced by Claypoole, Davis, Sweldens and Baraniuk, into lifting steps. We name the new wavelet family as invertible update-then-predict integer lifting wavelets (IUPILWs for short). To build IUPILWs, we investigate some central issues...

(Abstract) This dissertation is devoted to the development of new flow-based formulations for the asymmetric traveling salesman problem (ATSP) and to the demonstration of their applicability in effectively solving some scheduling problems. The ATSP is commonly encountered in the areas of manufacturing planning and scheduling, and transportation logistics. The integration of decisions pertaining...

This report reduces the total number of lifting steps in a three-dimensional (3D) double lifting discrete wavelet transform (DWT), which has been widely applied for analyzing volumetric medical images. The lifting steps are necessary components in a DWT. Since calculation in a lifting step must wait for a result of former step, cascading many lifting steps brings about increase of delay from in...

This study recruited eleven healthy males and thirteen healthy females to examine their maximum two-handed isometric back lifting strength, upper-body lifting strength, arm lifting strength and shoulder lifting strength in three different horizontal distances of objects to be lifted (toes were anterior to, aligned with, and posterior to the exerted handle). The results showed that human lifting...

The polyphase-with-advance matrix representations of whole-sample symmetric (WS) unimodular filter banks form a multiplicative matrix Laurent polynomial group. Elements of this group can always be factored into lifting matrices with half-sample symmetric (HS) off-diagonal lifting filters; such linear phase lifting factorizations are specified in the ISO/IEC JPEG 2000 image coding standard. Half...

We introduce the concepts of lifting modules and (quasi-)discrete modules relative to a given left module. We also introduce the notion of SSRS-modules. It is shown that (1) if M is an amply supplementedmodule and 0→N ′ →N →N ′′ → 0 an exact sequence, then M isN-lifting if and only if it isN ′-lifting andN ′′-lifting; (2) ifM is a Noetherianmodule, then M is lifting if and only if M is R-liftin...

This thesis addresses the problem of constructing a discrete wavelet approximating the shape of a given pattern. For the design of a biorthogonal wavelet basis we present an approach, which is based on the lifting scheme. The lifting scheme is a parametrisation of all biorthogonal wavelets. It reduces our problem to a linear least squares problem. The special structure of the problem allows for...