Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filter banks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar 2-channel wavelet systems. After reviewing this recently developed theory, we examine the use of multiwavelets in a filter bank setting for discrete-time signal and image processing. Multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filter bank. We describe two methods (repeated row and approximation/deapproximation) for obtaining such a vector input stream from a one-dimensional signal. Algorithms for symmetric extension of signals at boundaries are then developed, and naturally integrated with approximation-based preprocessing. We describe an additional algorithm for multiwavelet processing of two-dimensional signals, two rows at a time, and develop a new family of multiwavelets (the constrained pairs) that is well-suited to this approach. This suite of novel techniques is then applied to two basic signal processing problems, denoising via wavelet-shrinkage, and data compression. After developing the approach via model problems in one dimension, we applied multiwavelet processing to images, frequently obtaining performance superior to the comparable scalar wavelet transform.

H.264/MPEG-4 AVC is the latest international video coding standard. It was jointly developed by the Video Coding Experts Group (VCEG) of the ITU-T and the Moving Picture Experts Group (MPEG) of ISO/IEC. It uses state-of-the-art coding tools and provides enhanced coding efficiency for a wide range of applications including video telephony, video conferencing, TV, storage (DVD and/or hard disk based, especially high-definition DVD), streaming video, digital video authoring, digital cinema, and many others. The work on a new set of extensions to this standard has recently been completed. These extensions, known as the Fidelity Range Extensions (FRExt), provide a number of enhanced capabilities relative to the base specification as approved in the Spring of 2003. In this paper, an overview of this standard is provided, including the highlights of the capabilities of the new FRExt features. Some comparisons with the existing standards, MPEG-2 and MPEG-4 Part 2, are also provided.

Abstract. The refinement equation ϕ(t) = N 2 k=N 1 c k ϕ(2t − k) plays a key role in wavelet theory and in subdivision schemes in approximation theory. Viewed as an expression of linear dependence among the time-scale translates, it is natural to ask if there exist similar dependencies among the time-frequency translates e 2πibt f (t + a) of f ∈ L 2 (R). In other words, what is the effect of replacing the group representation of L 2 (R) induced by the affine group with the corresponding representation induced by the Heisenberg group? This paper proves that there are no nonzero solutions to lattice-type generalizations of the refinement equation to the Heisenberg group. Moreover, it is proved that for each arbitrary finite collectionis independent is an open, dense subset of L 2 (R). It is conjectured that this set is all of L 2 (R) \ {0}.

This paper investigates the asymptotic decay of the singular values of compact operators arising from the Weyl correspondence. The motivating problem is to find sufficient conditions on a symbol which ensure that the corresponding operator has singular values with a prescribed rate of decay. The problem is approached by using a Gabor frame expansion of the symbol to construct an approximating finite rank operator. This establishes a variety of sufficient conditions for the associated operator to be in a particular Schatten class. In particular, an improvement of a sufficient condition of Daubechies for an operator to be trace-class is obtained. In addition, a new development and improvement of the Caldero n Vaillancourt theorem in the context of the Weyl correspondence is given. Additional results of this type are then obtained by interpolation.

Public reporting burden for this collection of information is estimated to average I houri per resOpnse. including the time for reviewing Instructions. searching existing data sources,. gathering and maintaining the data needed, and completing and reviewing the collection of information Send comments rearding this burden estimate or any other aspect of this Approved for public release; distribution unlimited A ABSTRACT (Maximum 200 word)A technique of producing signals whose energy is concentrated in a given region of the time-frequency plane is examined. The degree to which a particular signal is concentrated is measured by integrating the Wigner distribution over the given region.This procedure was put forward by Flandrin, and has been used for timevarying filtering in the recent work of Hlawatsch, Kozek, and Krattenthaler. In this paper, the associated operator is studied.Estimates for the eigenvalue decay and the smoothness and decay of the eigenfunctions are established. MITREApproved for public release;Bedford, Massachusetts distribution unlimited. ABSTRACTA technique of producing signals whose energy is concentrated in a given region of the time-frequency plane is examined. The degree to which a particular signal is concentrated is measured by integrating the Wigner distribution over the given region. This procedure was put forward by Flandrin, and has been used for time-varying filtering in the recent work of Hlawatsch, Kozek, and Krattenthaler. In this paper, the associated operator is studied. Estimates for the eigenvalue decay and the smoothness and decay of the eigenfunctions are established.iii