Joint Detection and Estimation of Speech Spectral Amplitude Using Noncontinuous Gain Functions

This paper addresses the joint detection and estimation approach for single-channel speech enhancement. In this approach, a detector decides on speech presence in each time-frequency unit and an estimator estimates the corresponding speech spectral amplitude. We utilize the concept of binary/continuous gain functions to study and extend the process of joint detection and estimation. The binary gains (BGs) have already shown an inferior performance compared to the continuous gains (CGs). In this paper, we propose a simultaneous detection and estimation (SDE) method where the detector structure is derived by the knowledge of the estimator. The proposed SDE method is a combination of Bayesian and Neyman-Pearson approaches and is expressed as a noncontinuous gain (NCG). It is expected that employing a superior detector, the proposed NCG improves the quality of the output speech. We concentrate on the derivation of the detector so that it minimizes the error caused by missed detection and/or wrong estimation of speech coefficients at a controlled level of falsely detecting high-energy noise as speech. Furthermore, an independent detection and estimation technique is proposed where the detector and the estimator are extracted in an independent manner. Simulation results demonstrate that the proposed SDE method minimizes the speech distortion at a controlled level of noise reduction. It is also shown that the performance of the proposed NCG is better than the CG and than the existing BGs in both noise reduction and speech distortion aspects.