PROSE: Perceptual Risk Optimization for Speech Enhancement

The goal in speech enhancement is to obtain an estimateof clean speech starting from the noisy signal by minimizing a chosendistortion measure, which results in an estimate that depends onthe unknown clean signal or its statistics. Since access to suchprior knowledge is limited or not possible in practice, one hasto estimate the clean signal statistics. In this paper, we developa new risk minimization framework for speech enhancement, inwhich, one optimizes an unbiased estimate of the distortion/riskinstead of the actual risk. The estimated risk is expressed solely as afunction of the noisy observations. We consider several perceptuallyrelevant distortion measures and develop corresponding unbiasedestimates under realistic assumptions on the noise distribution anda priori signal-to-noise ratio (SNR). Minimizing the risk estimatesgives rise to the corresponding denoisers, which are nonlinearfunctions of the a posteriori SNR. Perceptual evaluation of speechquality (PESQ), average segmental SNR (SSNR) computations, andlistening tests show that the proposed risk optimization approachemploying Itakura-Saito and weighted hyperbolic cosine distortionsgives better performance than the other distortion measures. ForSNRs greater than 5 dB, the proposed approach gives superiordenoising performance over the benchmark techniques based on theWiener filter, log-MMSE minimization, and Bayesian nonnegativematrix factorization.Index Terms — Speech enhancement, perceptual distortion measure,unbiased risk estimation, Stein’s lemma, objective and subjectiveassessment.