The use of a paraunitary lter bank for image processing requires a special treatment at image boundaries to ensure perfect reconstruction and orthogonality of these regions. Using time-varying boundary lter banks, we will discuss a procedure that explores all degrees of freedom of the border lters in a method essentially independent of signal extensions, allowing us to design optimal boundary l...

New expressions are developed for the perfect reconstruction of the boundary regions of a finite-length signal after subband processing. The time-invariant filter bank is required to be uniform and paraunitary, using FIR filters regardless of phase or symmetry. They accomodate a linear boundary extension in the analysis section, and avoid periodic extensions or storage of extended subband signa...

In this paper we connect the design of biorthogonal modulated filter banks with the idea of lifting schemes, which were proposed for the construction of biorthogonal wavelets. Based on this formulation, we derive a lattice-like structure for the polyphase components. As the rotationbased structures for the design and implementation of paraunitary modulated filter banks, our structure automatica...

This paper presents boundary optimization techniques for the processing of arbitrary-length signals with paraunitary multirate filter banks. The boundary filters are designed to maximize the coding gain while providing an ideal DC behavior. Thus, all filters except the lowpass filter are designed to have zero mean. The proposed methods give direct solutions to the problem of finding optimal bou...

This paper surveys the progress made on pairwise orthogonal wavelet frames and comments on the construction methods. There are a few known constructions based on the unitary extension principle, a paraunitary matrix and a given modulation matrix. A polyphase matrix based construction method has been presented which satisfies the condition of unitary extension principle yielding pairwise orthogo...

In applications using multiwavelets there is a necessary step of associating a given discrete signal with a function in the scaling function space V 0. This association is equivalent to including a preelter and a posttl-ter for the lterbank determined by the underlying multiwavelets. We give a construction for FIR orthogonal (paraunitary) preelters that preserve the approximation order of a giv...

Cyclic signal processing refers to situations where all the time indices are interpreted modulo some integer L. In such cases, the frequency domain is defined as a uniform discrete grid (as in L-point DFT). This offers more freedom in theoretical as well as design aspects. While circular convolution has been the centerpiece of many algorithms in signal processing for decades, such freedom, espe...

| In applications using multiwavelets, there is a necessary step of associating a given discrete signal with a function in the scaling function space V 0. This association is equivalent to including a preelter and a posttlter for the lterbank determined by the underlying multiwavelets. We give a construction for orthogonal (paraunitary) FIR pre-lters that preserve the approximation order of a g...