Multiple channel shaping and its applications to signal restoration

The Viterbi algorithm is the optimum method for detection of a data sequence in the presence of intersymbol interference and additive Gaussian noise. However, its computational complexity is very large, about $M\sp{L}$, where M is the size of the signal set and L is the length of the channel impulse response. To mitigate the decoder complexity several simplifications and alternative methods have been proposed, most of which are more effective when dealing with minimum phase channels. We are primarily concerned with the case of high-speed digital transmission over HF radio channels under fast time-varying frequency selective fading conditions. From the combined effect of multipath and Doppler spread, it follows that we often need to address the problem of nonminimum phase channels. In this work we present a novel technique for the equalization of nonminimum phase channels which employs noncausal allpass filters operating in reversed time. The impulse response of the equalized channel approximates a minimum phase sequence with higher energy concentration at its left-hand end than at the right-hand end. The method is very effective not only in the case of two-path channels but also when more paths are present. It does not require computation of zeros of the channel impulse response, and the channel noise level is not enhanced. Moreover, the method is well suited to "sharpen" the channel impulse response with only minor variations in noise level, providing significant complexity reduction in the Viterbi algorithm for detection. In addition, a two-pass decoding strategy is developed, leading to significant improvement in performance with little increase in computational cost. Our noncausal equalization approach can also be effectively applied to deghosting of television signals and we examine the equalization of the multipath distortion for the case of digital transmission and nonminimum phase channels. In a noisy environment the deghosted images are often corrupted by impulse noise and the problem of restoring the image while preserving details and features needs to be addressed. Finally, a new framework for removing impulse noise from highly corrupted images is developed in which the filtering operation is conditioned on the differences between the input pixel and the remaining rank-ordered pixels in a sliding window. The method achieves excellent tradeoff between the suppression of noise and preservation of details and edges without undue increases in computational complexity. Moreover, it can effectively restore images corrupted with Gaussian noise and mixed Gaussian and impulse noise. Throughout this work, simulation results are included to verify the theoretical advantages of the proposed techniques.