# Wiener Filter and Deep Neural Networks: A Well-Balanced Pair for Speech Enhancement
###### Abstract  
This paper proposes a Deep Learning (DL) based Wiener filter estimator for speech enhancement in the framework of the classical spectral-domain speech estimator algorithm. According to the characteristics of the intermediate steps of the speech enhancement algorithm, i.e., the SNR estimation and  
based estimations of the SNR and the gain function. The work of [PERSON] et al. [8; 9] firstly approach the DNN-based SE by supporting the Wiener filtering with a weighted denoising autoencoder. This estimates the clean speech by subband and then uses it for estimating the short-term a priori SNR and the filter gain function. Similarly, from the mono-aural speech separation, the t-f masking approach with ideal binary/ratio masking (IBM/IRM) [10] is used for performing feature enhancement in automatic speech recognition (ASR) [3; 11]. In [12; 13], the authors proposed a supervised learning algorithm for IRM estimation to perform noise-robust ASR. Then, [PERSON]. [14; 15; 16; 17] extensively used the DL-based estimation of IBM and IRM for hearing-aids purposes also applied to ASR. For cochlear implant applications, [PERSON]. [18; 19; 20] extended the SE using DNN based on IRM to novel speakers and proposed an approach suitable for practical applications with low latency. Recently, DeepMMSE [21] attempted to estimate the power spectral density (PSD) of non-stationary noise using deep learning and they obtained very promising results. Related to this work, in [22], the authors estimated the a priori SNR with a residual long short-term memory (ResLSTM) network, achieving improvement in the performance of traditional minimum mean square error (MMSE) estimators. More recently, the same authors extended the study by including more architectures, such as residual networks and multi-head attention [23] and also using multiple objective quality and intelligibility measures to achieve improved enhancements of the noisy speech. This paper proposes a deep learning (DL) based approach to estimate the Wiener filter function and perform SE supported on the classical LSA speech estimator. We tested the performance by using directly the LSA speech estimator and also its optimally modified version (OMLSA) [24], which considers the speech presence probability (SPP). During the study, we explored the key points of the SE algorithm and accordingly the best use of deep learning. In [21; 22; 23], the deep learning approach targets the estimation of the a priori SNR, which is complemented with a compression function for making possible the training of the network. Then, the authors employed the a priori SNR estimation for computing the Wiener filter and proceed with the SE traditional algorithm. By analyzing this strategy, we realized that the high dynamic range of the SNR \((-\infty,\infty)\) is a hard objective to accurately be estimated by a deep structured network. This is the reason why a compression function was employed in [23] to avoid convergence problems during the training. Furthermore, SNR is an intermediate step to finally obtaining the Wiener filter function to feed the SE algorithm. So, it is more practical that the network was able to provide a more robust estimation of directly learning the Wiener filter. The main contribution of this paper relies on the use of the deep learning approach for directly estimating the Wiener filter instead of the a priori/posteriori SNR, which could bring accuracy and convergence troubles at the training step. Further contributions of this paper are as follows:  
* A data-driven Wiener filter estimator that can be generalized to different approaches of the classical spectral-domain speech estimator algorithm, tested with LSA and OMLSA speech estimators. * In the line of previous works, this paper demonstrates the usefulness of deep learning for expanding the application scope of established speech enhancement schemes in realistic scenarios with challenging environmental noisy patterns.