Signal restoration by spectral mapping

Traditional approaches to the problem of noise suppression or signal restoration have been almost entirely based upon the methodology and theory of signal estimation. In this paper, we treat signal restoration as a problem in signal detection. Instead of estimating the characteristics of the signal and/or the noise, we establish a correspondence between the clean and the noisy signal through spectral mapping. In the procedure, we collect separate samples of both the clean signal and the noise. When the noise is additive, the (simulated) noisy signal is obtained by adding the noise to the clean signal. The sequence of short time spectra of the clean signal and that of the noisy signal form a one-to-one correspondence. The noisy spectral sequence is then used as a detection reference, to which the short time spectrum of an unknown noisy observation is compared, resulting in a detected occurrence of a particular group of spectra in the noisy sequence. Through the (inverse) mapping, the clean spectra that correspond to the detected noisy spectra are selected and processed to produce the restored spectrum. One important notion of the approach is that it is not limited to the usual least squares or minimum mean square framework. Our preliminary results show that when the mapping (detection) is based upon the likelihood ratio distortion measure, an SNR improvement of approximately 10 dB is obtainable for a 14 dB SNR noisy signal. Under the same condition, an improvement of approximately 8.5 dB can be obtained using a truncated cepstral distance measure.