Fast optimal signal representations and their applications

Chuan-Hsing Chen, Purdue University

Abstract

The purpose of this research is to develop methodologies for fast optimal representation of signals for applications in image compression and neural networks. The optimal transform in linear systems is Karhunen-Loeve transform (KLT). KLT will be approximated by a fast transform (FT). One way to achieve this is by specifying a sequence of permutations of the input signal, a know fast transform based on a priori information (such as one of generalized real discrete Fourier transforms), a second sequence of permutations and a small number of Jacobi rotations. We can generalize the idea by skipping the known fast transform and designing successive stages of permutations and rotations. For different signals, i.e. different covariance matrices, we use the method of simulated annealing to find the optimal permutation matrices. Plane rotations are found by using the Jacobi method. Our results show that the scrambled real discrete Fourier transform (SRDFT), one of the FT, has basically the same visual performance as the discrete cosine transform (DCT) in image compression, with much lower complexity of operations. The interaction between neural networks and fast transforms is presented. It is shown that the development, discovery and study of new transforms can be efficiently carried out through the use of learning algorithms used in neural networks. In turn, these transforms can be used for a number of tasks in neural networks such as network reduction and simplification, fast convergence during learning, fast memory retrieval, reduced cost and increased speed of implementation, feature extraction, invariance to distortions, better generalization and increased quality of performance in the presence of noise and incomplete knowledge. Learning with the unconstrained part of the neural network of reduced size or minimized number of interconnections is performed in the spectral domain only, thereby considerably easing the problems of convergence and implementation. The techniques described can be especially useful in dynamic neural networks. Fast optimal representation of signals in the spectral domain and their performance in image compression and neural networks will be further studied and compared.

Degree

Ph.D.

Advisors

Ersoy, Purdue University.

Subject Area

Electrical engineering

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