A new realization of 2-D adaptive separable-denominator state-space filters based on DLMS algorithm suitable for parallel processing☆
Introduction
An adaptive filter has been applied to various fields of signal processing, such as echo canceller, system identification and adaptive equalizer. Nowadays, it also has been extended to process multi-dimensional signals for the purpose of the noise reduction of image data, multi-dimensional system identification and multi-dimensional digital filter design, which results that multi-dimensional adaptive filters have been proposed and their researches are getting more popular [8], [10], [11], [12]. One concern, however, is that a multi-dimensional adaptive filter not only has to process a large amount of data, like an image, but sometimes has to perform real-time processing to handle such large data. Therefore, high-speed processing should be required for high-dimensional adaptive filters. One of the ideas for that is to apply the parallel processing structure of adaptive filters.
For 2-D digital filters, several methods suitable for the parallel processing have been proposed [1], [2]. Besides, we have some studies on 2-D adaptive filters suitable for the parallel processing where 2-D digital filter for parallel processing is applied to the structure of 2-D adaptive filters [3], [4], [5] and also extended to 3-D case [6].
This paper proposes a new parallel-form realization of a 2-D adaptive filter based on the Roesser local state-space model with separable denominator. The DLMS algorithm [7] is adopted as an adaptive algorithm in this realization. The class of separable denominator is one of the most important classes, since almost frequency specification can be implemented. The effective parallel form realization can also be achieved. However, such realizations by the general local state-space model are difficult because of its complicated feedback structure.
At first, the parallel-form realization of a 2-D digital filter with separable denominator proposed by Dabbagh and Alexander [1] is brought up for consideration. Then, a new adaptive algorithm is introduced by the combination of the DLMS algorithm and the adaptive algorithm for a 2-D state-space digital filter with separable denominator [8]. The computational time required for the filtering and the coefficient update is also evaluated to prove that the use of the DLMS algorithm leads a faster algorithm than the algorithms reported in [3], [4]. Finally, the effectiveness of the proposed technique is confirmed by applying it to 2-D digital filter design in the spatial domain.
Section snippets
Parallel implementation of 2-D state-space filters with separable denominator
In this section, the parallel-form implementation of 2-D state-space filter with separable denominator reported in [5] is introduced to be prepared for deriving the corresponding adaptive algorithm [9].
Consider the following irreducible 2-D separable-denominator transfer function:where
The 2-D separable denominator transfer function expressed in Eq. (1) can be represented by
Adaptive algorithm and its evaluation
In this section, an adaptive algorithm derived from the DLMS algorithm and the corresponding computational time is estimated in order to show the effect of the parallel processing.
Simulation
To demonstrate the effectiveness of the proposed algorithm, we have carried out the simulation applied to 2-D digital filter design in the spatial domain.
The unit sample response of the Gaussian filter is given by the following equation:whereThe order of the filter was chosen as M=N=3, and the input signal was assumed to beThe step-size parameter was chosen to be μ=0.0007 and
Conclusion
The new parallel-form realization of 2-D adaptive filters, based on the Roesser local state-space model with separable denominator, has been proposed. The DLMS method has been applied to implement the adaptive algorithm and proved out to reduce the minimum computation time for each input. The proposed adaptive filter has been developed by combining the parallel-form realization with the adaptive algorithm for 2-D separable-denominator digital filters. Also, the computational time required for
References (12)
- et al.
A 2-D cascade-parallel adaptive IIR filter using backpropagation method
J. Franklin Institute
(1996) - et al.
Multiprocessor implementation of 2-D denominator-separable digital filters for real-time processing
IEEE Trans. Acoust. Speech Signal Process.
(1989) - et al.
Realization of 2-D separable-denominator digital filters for real-time and parallel processing
Trans. IEICE, J74-A
(1991) - et al.
Parallel-from realization of 2-D adaptive separable-denominator state-space filters
Trans. IEICE J77-A
(1994) - M. Muneyasu, N. Ishizaki, T. Hinamoto, A realization of 2-D adaptive separable-denominator state-space filters for...
- M. Muneyasu, N. Ishizaki, T. Hinamoto, A realization of 3-D adaptive separable-denominator state-space filters for...
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The results in this paper were partially presented at the 1998 IEEE International Workshop on Intelligent Signal Processing and Communication Systems.