Tsuhan Chen

Role of anticausal inverses in multirate filter-banks .I. System-theoretic fundamentals

In a maximally decimated filter bank with identical decimation ratios for all channels, the perfect reconstructibility property and the nature of reconstruction filters (causality, stability, FIR property, and so on) depend on the properties of the polyphase matrix. Various properties and capabilities of the filter bank depend on the properties of the polyphase matrix as well as the nature of its inverse. In this paper we undertake a study of the types of inverses and characterize them according to their system theoretic properties (i.e., properties of state-space descriptions, McMillan degree, degree of determinant, and so forth). We find in particular that causal polyphase matrices with anticausal inverses have an important role in filter bank theory. We study their properties both for the FIR and IIR cases. Techniques for implementing anticausal IIR inverses based on state space descriptions are outlined. It is found that causal FIR matrices with anticausal FIR inverses (cafacafi) have a key role in the characterization of FIR filter banks. >

Multidimensional multirate filters and filter banks derived from one-dimensional filters

A method by which every multidimensional (M-D) filter with an arbitrary parallelepiped-shaped passband support can be designed and implemented efficiently is presented. It is shown that all such filters can be designed starting from an appropriate one-dimensional prototype filter and performing a simple transformation. With D denoting the number of dimensions, the complexity of design and implementation of the M-D filter are reduced from O(N/sup D/) to O(N). Using the polyphase technique, an implementation with complexity of only 2N is obtained in the two-dimensional. Even though the filters designed are in general nonseparable, they have separable polyphase components. One special application of this method is in M-D multirate signal processing, where filters with parallelepiped-shaped passbands are used in decimation, interpolation, and filter banks. Some generalizations and other applications of this approach, including M-D uniform discrete Fourier transform (DFT) quadrature mirror filter banks that achieve perfect reconstruction, are studied. Several design example are given. >

Recent developments in multidimensional multirate systems

The authors review the fundamentals of multidimensional (M-D) multirate signal processing and present recent and new developments in M-D multirate systems. A method is presented for deriving all parallelepiped-shaped filters in M-D multirate applications from an appropriate 1-D filter. It is shown that the generalized-pseudocirculant property is necessary and sufficient for an M-D maximally decimated filter-bank system to be free from aliasing. It is shown how the Smith form, Smith-McMillan form, and the least common multiples of integer matrices can resolve many nonseparable M-D multirate problems. The condition for alias-free decimation and the multistage design of decimation systems are mentioned. >

Role of anticausal inverses in multirate filter-banks .II. The FIR case, factorizations, and biorthogonal lapped transforms

For pt. I see ibid., vol.43, no.5, p.1090, 1990. In part I we studied the system-theoretic properties of discrete time transfer matrices in the context of inversion, and classified them according to the types of inverses they had. In particular, we outlined the role of causal FIR matrices with anticausal FIR inverses (abbreviated cafacafi) in the characterization of FIR perfect reconstruction (PR) filter banks. Essentially all FIR PR filter banks can be characterized by causal FIR polyphase matrices having anticausal FIR inverses. In this paper, we introduce the most general degree-one cafacafi building block, and consider the problem of factorizing cafacafi systems into these building blocks. Factorizability conditions are developed. A special class of cafacafi systems called the biorthogonal lapped transform (BOLT) is developed, and shown to be factorizable. This is a generalization of the well-known lapped orthogonal transform (LOT). Examples of unfactorizable cafacafi systems are also demonstrated. Finally it is shown that any causal FIR matrix with FIR inverse can be written as a product of a factorizable cafacafi system and a unimodular matrix. >

Lip synchronization using speech-assisted video processing

We utilize speech information to improve the quality of audio-visual communications such as videotelephony and videoconferencing. In particular, the marriage of speech analysis and image processing can solve problems related to lip synchronization. We present a technique called speech-assisted frame-rate conversion. Demonstration sequences are presented. Other applications, including speech-assisted video coding, are outlined.<<ETX>>

The role of integer matrices in multidimensional multirate systems

Various theoretical issues in multidimensional (m-D) multirate signal processing are formulated and solved. In the problems considered, the decimation matrix and the expansion matrix are nondiagonal, so that extensions of 1-D results are nontrivial. The m-D polyphase implementation technique for rational sampling rate alterations, the perfect reconstruction properties for the m-D delay-chain systems, and the periodicity matrices of decimated m-D signals (both deterministic and statistical) are treated. The discussions are based on several key properties of integer matrices, including greatest common divisors and least common multiples. These properties are reviewed. >

Defocus-based image segmentation

Foreground and background features are focused (or defocused) differently in an image because corresponding objects are at different depths in the scene. This paper presents a novel approach for segmenting foreground and background in video images based on feature defocus. A modified defocus measurement that distinguishes between high-contrast defocused edges and low-contrast focused edges is presented. Defocus-based segmentation is desirable because defocus techniques are computationally simple. Results indicate that the foreground is easily segmented from moving background. This approach, coupled with motion detection, can segment complex scenes containing both moving background and stationary foreground.

A new frame interpolation scheme for talking head sequences

A video codec typically-skips frames to satisfy the bit rate constraint. This results in a jerky motion and a loss of lip synchronization in sequences of talking persons. We propose a frame interpolation technique to solve these problems. The main components of this technique include: foreground/background segmentation, mesh-based frame interpolation, and image analysis/synthesis for mouth movements. This technique generates smooth head motion and renders lip motion that is synchronized with the voice of the person.

Vector space framework for unification of one- and multidimensional filter bank theory

A number of results in filter bank theory can be viewed using vector space notations. This simplifies the proofs of many important results. In this paper, we first introduce the framework of vector space, and then use this framework to derive some known and some new filter bank results as well. For example, the relation among the Hermitian image property, orthonormality, and the perfect reconstruction (PR) property is well-known for the case of one-dimensional (1-D) analysis/synthesis filter banks. We can prove the same result in a more general vector space setting. This vector space framework has the advantage that even the most general filter banks, namely, multidimensional nonuniform filter banks with rational decimation matrices, become a special case. Many results in 1-D filter bank theory are hence extended to the multidimensional case, with some algebraic manipulations of integer matrices. Some examples are: the equivalence of biorthonormality and the PR property, the interchangeability of analysis and synthesis filters, the connection between analysis/synthesis filter banks and synthesis/analysis transmultiplexers, etc. Furthermore, we obtain the subband convolution scheme by starting from the generalized Parsevals relation in vector space. Several theoretical results of wavelet transform can also be derived using this framework. In particular, we derive the wavelet convolution theorem. >

Statistically optimal synthesis banks for subband coders

In maximally decimated filter banks, the perfect reconstruction or biorthogonal solution is not necessarily the best choice when subband quantizers are present. Under suitable statistical assumptions, expressions for the best synthesis bank can be derived in terms of the analysis bank and other statistical quantities. We explore this topic for subband coders and the special case of transform coders. We highlight the statistical conditions under which the biorthogonal solution is still the best. We derive expressions for the Wiener filter matrix in terms of the joint statistics of appropriate signals. Special cases where the optimal synthesis filter bank is the biorthogonal system followed by a scalar post filter are also considered.<<ETX>>