Linear-phase perfect reconstruction filter bank: lattice structure, design, and application in image coding

Abstract

A lattice structure for an-channel linear-phase perfect reconstruction filter bank (LPPRFB) based on the singular value decomposition (SVD) is introduced. The lattice can be proven to use a minimal number of delay elements and to completely span a large class of LPPRFB's: All analysis and synthesis filters have the same FIR length, sharing the same center of symmetry. The lattice also structurally enforces both linear-phase and perfect reconstruction properties, is capable of providing fast and efficient implementation, and avoids the costly matrix inversion problem in the optimization process. From a block transform perspective, the new lattice can be viewed as representing a family of generalized lapped biorthogonal transform (GLBT) with an arbitrary number of channels and arbitrarily large overlap. The relaxation of the orthogonal constraint allows the GLBT to have significantly different analysis and synthesis basis functions, which can then be tailored appropriately to fit a particular application. Several design examples are presented along with a high-performance GLBT-based progressive image coder to demonstrate the potential of the new transforms. I. INTRODUCTION T HERE HAS been a tremendous growth in the field of filter banks (FB's) and multirate systems in the last 15 years. These systems provide new and effective ways to represent signals for processing, understanding, and compression purposes. Filter banks find applications in virtually every signal processing field [1]-[3]. Obviously, of extreme importance is the ability to design a filter bank that can fully exploit the properties and nature of a particular class of signals or applications. In this paper, we consider the discrete-time maximally decimated-channel uniform filter bank as depicted in Fig. 1(a). At the analysis stage, the input signal is passed through a bank of analysis filters , each of which preserves a frequency band of uniform bandwidth. These filtered signals are then decimated by to preserve the system's overall

Image analysis using a dual-tree M-band wavelet transform

“…(19). Asα 0,m is a 2π/M -periodic function, it is fully defined by its expression on [0, (13) and (17), we obtain, for all m ∈ {0, .…”

“…The relative sparsity of good filter banks amongst all possible solutions is also well-known. In order to improve both design freedom and filter behavior, M -band filter banks and wavelets have been proposed [17]- [19].…”

<title>Fast-lapped transform for image coding</title>

“…(10) can be proven to be minimal, i.e., the resulting lattice employs the least number of delays in the implementation. 9 We use the term variable length GLBT or VLGLBT to refer to such a structure. Of course, more VL structuresĜ i (z) can be added to increase the frequency resolution of the long filters.…”

“…However, as compression increases, the reconstructed image is often subjected to blocking and ringing artifacts. The development of the lapped orthogonal transform (LOT), 2 its generalized version GenLOT, 3 and the extensions to biorthogonality [4][5][6][7] help solve the blocking problem by borrowing pixels from the adjacent blocks to produce the transform coefficients of the current block. Lapped transforms outperform the DCT on two counts: (i) from the analysis viewpoint, it takes into account inter-block correlation, hence, provides better energy compaction; (ii) from the synthesis viewpoint, its basis functions decay asymptotically to zero at the ends, reducing blocking discontinuities drastically.…”

On Filter Symmetries in a Class of Tree-Structured 2-D Nonseparable Filter-Banks

“…N the one-dimensional (1-D) case, filter-banks (FBs) with filters having symmetries or anti-symmetries, 1 which lead to linear-phase FBs, are commonly used for image processing and coding applications, and design of such 1-D linear-phase FBs has been extensively addressed in the literature (see [1], [9], [10], and references therein). Such symmetric filters are also important in 1-D symmetric signal extension schemes-which are used to maintain critical sampling when the input signal is of finite extent [4]- [6].…”