HomeChair: Palghat P. Vaidyanathan, California Institute of Technology, USA
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Omid S Jahromi, Shiraz University (Iran)
M. A Masnadi-Shirazi, Shiraz University (Iran)
Minyue Fu, University of Newcastle (Australia)
Designing optimal filter banks for subband coding applications has recently attracted considerable attention.In particular, the first two authors had developed an adaptive algorithm based on stochastic gradient descent (SGD) that enables one to optimize two-channel paraunitary filter banks in an on-line fashin [3]. They have also extended the adaptive algorithm for the case of tree-structured filter banks [4]. The computational complexity of the algorithm proposed originally is proportional to the seconed power of N, where N is the number of stages in the paraunitary lattice. In this paper, we derive a fast algorithm which reduces the amount of computation to O(N). We also show that the new algorithm can be implemented using an IIR lattice structure. Some issues regarding numerical stability of the proposed IIR implementation are also discussed.
ic981412.pdf (From Postscript)
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Ahmet Kirac, Caltech (U.S.A.)
Palghat P. Vaidyanathan, Caltech (U.S.A.)
In this paper we have two interesting results. One is of theoretical interest and the other practical. The theoretical result is that the optimum FIR orthonormal filter bank of a fixed finite degree that maximizes the coding gain does not always contain an optimum compaction filter. In other words, in general, there does not exist a principal component filter bank (PCFB) of a given nonzero degree. This is sharply in contrast to the cases of transfom coders and ideal subband coders where the existence of PCFB's are assured by their very construction. The practical result of the paper is that constraining the filter corresponding to the largest subband variance to be a compaction filter does not result in a significant loss of performance for practical input signals. Since there exist very efficient methods to design FIR compaction filters and since the best completion of the filter bank given the first filter is trivially done by a KLT, we see that this is an exteremely efficient method despite the fact that it is suboptimum.
ic981305.pdf (From Postscript) TOPWolfgang Niehsen, IENT, RWTH Aachen (Germany)
The energy compaction performance of two-channel paraunitary finite impulse response (FIR) filter banks for finite-length signals is investigated. A detailed non-iterative design procedure for boundary filters which are optimal in a weighted mean square error (MSE) sense in the Fourier domain is presented. Simulation results are given for two-channel paraunitary FIR filter banks based on minimum-phase Daubechies filters and least-asymmetric Daubechies filters, respectively.
ic981052.pdf (From Postscript) TOP
Are Hjørungnes, University of California, Santa Barbara (U.S.A.)
Tor A. Ramstad, University of California, Santa Barbara (U.S.A.)
A subband coder structure is fully optimized with respect to the minimum block mean squared error between the output and the input signals under a bit constraint. The analysis filter bank structure generates maximally decimated and equal bandwidth subbands. The subband quantizers are modeled as additive noise sources. To simplify the optimization an optimal multiple-input multiple-output system is first derived. Illustrative examples showing the system performance as well as filter transfer functions are given. The performance results are compared to the rate distortion curves.
ic982237.pdf (From Postscript) TOPRicardo L De Queiroz, Xerox Corporation (U.S.A.)
In this paper, uniform, critically decimated filter banks are used to approximate nonuniform filter banks wherein different filters have approximately the same magnitude response, but different phase, thus forming a linear periodically time-varying filter whose characteristics are similar to those of a nonuniform bank. This is done by post-processing a number of selected subbands of a uniform bank using a special synthesis filter bank, which combines the selected bands into one. Design methods for the post-processing stage are discussed and design examples are presented.
ic981083.pdf (From Postscript) TOP
Omer N Gerek, Bilkent University (Turkey)
A. Enis Cetin, Bilkent University (Turkey)
Subband decomposition techniques have been extensively used for data coding and analysis. In most filter banks, the goal is to obtain subsampled signals corresponding to different spectral bands of the original data. However, this approach leads to various artifacts in images containing text, subtitles, or sharp edges. In this paper, adaptive filter banks with perfect reconstruction property are presented for such images. The filters of the decomposition structure vary according to the nature of the signal. This leads to higher compression ratios for images containing subtitles compared to fixed filter banks. Simulation examples are presented.
ic981248.pdf (From Postscript) TOP
Ilangko Balasingham, Norwegian University of Science and Technology (Norway)
John M. Lervik, Fast Internet Transfer AS (Norway)
Tor A. Ramstad, University of California, Santa Barbara (U.S.A.)
A novel way of constructing integer coefficient 2-channel filter banks is proposed. A set of relationships among the filter coefficients is established in order to satisfy linear phase, perfect reconstruction, and FIR properties. The remaining degrees of freedom are used to obtain integer coefficient values by maximizing a performance evaluation function, namely subband coding gain. The number of bits required to represent the subband samples is kept low through efficient nonlinear implementation techniques. An octave-band frequency partitioning where the number of stages is determined according to the image size is employed. The subband samples are then classified into one out of a finite number of classes, and each class is coded by an arithmetic coder. The obtained compression ratios are encouraging compared to the ``best'' results reported so far in the literature.
ic981280.pdf (From Postscript) TOP
Jamal Tuqan, California Institute of Technology (U.S.A.)
Palghat P. Vaidyanathan, California Institute of Technology (U.S.A.)
We introduce a new approach to adapt a two-channel FIR orthonormal filter bank to the input second order statistics. The problem is equivalent to optimizing the magnitude squared response of one the subband filters for maximum energy compaction under the constraint that it is Nyquist(2). The novel algorithm enjoys important advantages that are not present in previous work. First, we can ensure the positivity of the resulting magnitude squared response over all frequencies simultaneously with the Nyquist constraint. Second, for a fixed input power spectrum, the resulting magnitude squared response is guaranteed to be a global optimum due to the convexity of the new formulation. The optimization problem is expressed as a multi-objective semi definite programming problem which can be solved efficiently and with great accuracy using recently developed interior point methods. Third, the new algorithm is extremely general in the sense that it works for any arbitrary filter order N and any given input power spectrum. Finally, obtaining the subband filter from its magnitude squared response does not require an additional spectral factorization step.
ic981846.pdf (From Postscript) TOP