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Impulse noise correction in an image transmission system by means of an oversampled filter bank code

Quantized frame expansions based on block transforms and oversampled filter banks (OFB) have been considered recently as joint source-channel codes for erasure and error resilient signal transmission over noisy channels. This paper examines the problem of syndrome decoding and especially of error localization and correction in quantized OFB signal expansions. The error localization problem is treated as an M-ary hypothesis testing problem. The tests are derived from the joint probability density function of the syndromes under various hypothesis of impulse noise positions and in a number of consecutive windows of the received samples (to account for the encoding memory of the convolutional code). The error amplitudes are then estimated from the syndrome equations by solving them in the least square sense. The message signal is reconstructed from the corrected received signal by a pseudoinverse receiver. The algorithm is applied to joint source and channel coding (JSCC) of images based on oversampled wavelet filter banks.