Universal Denoising of Discrete-time Continuous-Amplitude Signals

We consider the problem of reconstructing a discrete-time continuous-amplitude signal corrupted by a known memoryless channel with a general output alphabet. We develop a sequence of denoisers that asymptotically achieve optimum performance in a semi-stochastic setting of an unknown individual noiseless signal, where the quality of reconstruction is measured with respect to a general given loss function satisfying mild conditions. We also extend this to the fully stochastic setting and show that our denoiser is asymptotically optimal for any stationary noiseless source. We conclude with some experimental validations of the proposed theory