Adaptive signal processing
Speech enhancement from noise: a regenerative approach
Speech Communication
Adaptive filter theory (3rd ed.)
Adaptive filter theory (3rd ed.)
Toeplitz and circulant matrices: a review
Communications and Information Theory
ICASSP '91 Proceedings of the Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference
Acoustic MIMO Signal Processing (Signals and Communication Technology)
Acoustic MIMO Signal Processing (Signals and Communication Technology)
On the optimal linear filtering techniques for noise reduction
Speech Communication
EURASIP Journal on Applied Signal Processing
GSVD-based optimal filtering for single and multimicrophone speech enhancement
IEEE Transactions on Signal Processing
Wiener filters in canonical coordinates for transform coding,filtering, and quantizing
IEEE Transactions on Signal Processing
New insights into the noise reduction Wiener filter
IEEE Transactions on Audio, Speech, and Language Processing
Analysis and Comparison of Multichannel Noise Reduction Methods in a Common Framework
IEEE Transactions on Audio, Speech, and Language Processing
On the Importance of the Pearson Correlation Coefficient in Noise Reduction
IEEE Transactions on Audio, Speech, and Language Processing
Computers in Biology and Medicine
IEEE/ACM Transactions on Audio, Speech and Language Processing (TASLP)
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Noise reduction for speech applications is often formulated as a digital filtering problem, where the clean speech estimate is obtained by passing the noisy speech through a linear filter/ transform. With such a formulation, the core issue of noise reduction becomes how to design an optimal filter (based on the statistics of the speech and noise signals) that can significantly suppress noise without introducing perceptually noticeable speech distortion. The optimal filters can be designed either in the time or in a transform domain. The advantage of working in a transform space is that, if the transform is selected properly, the speech and noise signals may be better separated in that space, thereby enabling better filter estimation and noise reduction performance. Although many different transforms exist, most efforts in the field of noise reduction have been focused only on the Fourier and Karhunen-Loève transforms. Even with these two, no formal study has been carried out to investigate which transform can outperform the other. In this paper, we reformulate the noise reduction problem into a more generalized transform domain. We will show some of the advantages of working in this generalized domain, such as 1) different transforms can be used to replace each other without any requirement to change the algorithm (optimal filter) formulation, and 2) it is easier to fairly compare different transforms for their noise reduction performance. We will also address how to design different optimal and suboptimal filters in such a generalized transform domain.