Optimally regularized adaptive filtering algorithms for room acoustic signal enhancement

In many room acoustic signal processing applications, a room impulse response identification is needed to eliminate undesired effects such as echo, feedback, or reverberation. This is typically done using an adaptive filter driven by a speech or audio input signal. However, such signals exhibit poor excitation properties, which cause standard adaptive filtering algorithms to be very sensitive to disturbing signals, especially in the underdetermined case. A popular remedy is regularization, which is usually implemented with a scaled identity regularization matrix. This type of regularization is governed by a single regularization parameter, the value of which is often chosen in an arbitrary way. We propose to regularize the adaptive filter using a non-identity regularization matrix, in which prior knowledge on the unknown room impulse response may be incorporated. When knowledge of the disturbing signal is also used to add prefiltering and weighting in the adaptation, a new family of regularized adaptive filtering algorithms is obtained, which is shown to be optimal in a mean square error sense. Existing regularized algorithms can then be obtained as special cases, assuming limited or no prior knowledge is available. When combined with a recently proposed method of extracting prior knowledge from the acoustic setup, our algorithms exhibit superior convergence behaviour compared to existing algorithms in different simulation scenarios, while the additional computational cost is small.