Minimum Mean Square Error (MMSE) Speech Enhancement Algorithm

This document introduces the Minimum Mean Square Error (MMSE) speech enhancement algorithm. This algorithm demonstrates remarkable simplicity and effectiveness in eliminating residual musical noise while improving speech quality. The MMSE approach processes input signals through statistical estimation techniques to minimize noise impact, resulting in clearer and more intelligible speech output. In practical implementation, the algorithm typically involves calculating the spectral magnitude estimation using Wiener filter principles, where the clean speech spectrum is estimated based on noise statistics and signal-to-noise ratio (SNR) measurements. The core mathematical formulation involves minimizing the mean square error between the estimated and actual clean speech signals. This algorithm proves highly valuable in real-world applications, delivering superior speech enhancement performance across various environmental conditions. Therefore, employing the MMSE speech enhancement algorithm represents an effective methodology for quality improvement and residual musical noise elimination in audio processing systems.