# Crossband Filtering for Weighted Prediction Error-Based Speech Dereverberation
###### Abstract  
Weighted prediction error (WPE) is a linear prediction-based method extensively used to predict and attenuate the late reverberation component of an observed speech signal. This paper introduces an extended version of the WPE method to enhance the modeling accuracy in the time-frequency domain by incorporating crossband filters. Two approaches to extending the WPE while considering crossband filters are proposed and investigated. The first approach improves the model's accuracy. However, it increases the computational complexity, while the second approach maintains the same computational complexity as the conventional WPE while still achieving improved accuracy and comparable performance to the first approach. To validate the effectiveness of the proposed methods, extensive simulations are conducted. The experimental results demonstrate that both methods outperform the conventional WPE regarding dereverberation performance. These findings highlight the potential of incorporating crossband filters in improving the accuracy and efficacy of the WPE method for dereverberation tasks. crossband filtering; speech dereverberation; speech enhancement; weighted prediction error +
Footnote †: journal: Medical  
also been widely explored in dereverberation research. These methods operate in the frequency domain and aim to enhance the desired speech signal by modifying the spectral characteristics. One example is the spectral subtraction method [13; 14]. This technique estimates the noise and reverberation spectra and subtracts them from the observed signal to enhance the speech component. Other spectral enhancement approaches employ advanced signal processing methods such as Wiener filtering and statistical modeling to separate the desired speech from the interfering components [15]. Another category of dereverberation methods focuses on estimating an inverse filter to predict and suppress the late reflections present in the observed speech signal [16; 17; 18; 19; 20]. One notable method in this category that has gained significant attention in the field of speech processing is the weighted prediction error (WPE) method [19; 20]. WPE is based on linear prediction (LP), utilizing an inverse filter to estimate and suppress the late reflections in the observed speech signal. By exploiting the statistical properties of the reverberation, WPE effectively separates the desired speech component from the reverberant component. The method estimates the optimal filter coefficients by minimizing the prediction error between the observed signal and its predicted version. WPE has proven highly effective in various applications [21; 22]. Due to its effectiveness, WPE has received significant attention and has been extensively studied, leading to the proposal of numerous extensions, generalizations, and variants. For instance, in [20], the model formulation, which assumed a single speech source, was generalized to an arbitrary number of sources. Other extensions and generalizations include the employment of deep neural networks [23; 24], switching mechanisms [25], and Kronecker product filtering to improve the computational complexity [26]. In most applications, the WPE method is implemented in the short-time Fourier transform (STFT) domain, which provides a suitable framework for the analysis and processing of the observed speech signal. By decomposing the time-domain-observed signal into subbands, WPE operates on these subbands individually in a frequency-band-wise manner. In the time domain, WPE models the observed speech signal as the result of a linear convolution between the clean speech signal and an unknown room impulse response (RIR). However, when transitioning to the STFT domain, the relationship between the observed and clean signals becomes more intricate. In the STFT domain, the observed subbands are influenced not only by their corresponding clean subbands but also by the adjacent subbands and the crossband filters [27; 28].