Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> Wavelet Denoising <s> Donoho and Johnstone (1994) proposed a method for reconstructing an unknown function f on [0,1] from noisy data d/sub i/=f(t/sub i/)+/spl sigma/z/sub i/, i=0, ..., n-1,t/sub i/=i/n, where the z/sub i/ are independent and identically distributed standard Gaussian random variables. The reconstruction f/spl circ/*/sub n/ is defined in the wavelet domain by translating all the empirical wavelet coefficients of d toward 0 by an amount /spl sigma//spl middot//spl radic/(2log (n)/n). The authors prove two results about this type of estimator. [Smooth]: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures. [Adapt]: the estimator comes nearly as close in mean square to f as any measurable estimator can come, uniformly over balls in each of two broad scales of smoothness classes. These two properties are unprecedented in several ways. The present proof of these results develops new facts about abstract statistical inference and its connection with an optimal recovery model. > <s> BIB001 </s> Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> Wavelet Denoising <s> This paper presents an improved thresholding technique for speech enhancement in the discrete cosine transform (DCT) domain. The signal-bias-compensated noise level is used as the threshold parameter. The probability of speech presence in the noisy DCT coefficients at the finest level is exploited for compensating the signal-bias. The performance of the proposed algorithm is evaluated on speech corrupted by background Gaussian white noise and real noise recorded inside a moving car. A relative comparison in the enhancement of the degraded speech is performed using the uncompensated and compensated noise levels for the same denoising filter. Both objective and subjective evaluations are presented to show improved performance for the case when the compensated noise level, estimated by the proposed algorithm, is used rather than the uncompensated noise level obtained using the median absolute deviation method. Simulation results are also given to show the superiority of the proposed method over a recently reported enhancement algorithm. <s> BIB002 </s> Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> Wavelet Denoising <s> Most speech enhancement algorithms are based on the assumption that speech and noise are both Gaussian in the discrete cosine transform (DCT) domain. For further enhancement of noisy speech in the DCT domain, we consider multiple statistical distributions (i.e., Gaussian, Laplacian and Gamma) as a set of candidates to model the noise and speech. We first use the goodness-of-fit (GOF) test in order to measure how far the assumed model deviate from the actual distribution for each DCT component of noisy speech. Our evaluations illustrate that the best candidate is assigned to each frequency bin depending on the Signal-to-Noise-Ratio (SNR) and the Power Spectral Flatness Measure (PSFM). In particular, since the PSFM exhibits a strong relation with the best statistical fit we employ a simple recursive estimation of the PSFM in the model selection. The proposed speech enhancement algorithm employs a soft estimate of the speech absence probability (SAP) separately for each frequency bin according to the selected distribution. Both objective and subjective tests are performed for the evaluation of the proposed algorithms on a large speech database, for various SNR values and types of background noise. Our evaluations show that the proposed soft decision scheme based on multiple statistical modeling or the PSFM provides further speech quality enhancement compared with recent methods through a number of subjective and objective tests. <s> BIB003 </s> Temporal and Spectral Processing Methods for Processing of Degraded Speech: A Review <s> Wavelet Denoising <s> In this paper, we proposed a new speech enhancement system, which integrates a perceptual filterbank and minimum mean square error-short time spectral amplitude (MMSE-STSA) estimation, modified according to speech presence uncertainty. The perceptual filterbank was designed by adjusting undecimated wavelet packet decomposition (UWPD) tree, according to critical bands of psycho-acoustic model of human auditory system. The MMSE-STSA estimation (modified according to speech presence uncertainty) was used for estimation of speech in undecimated wavelet packet domain. The perceptual filterbank provides a good auditory representation (sufficient frequency resolution), good perceptual quality of speech and low computational load. The MMSE-STSA estimator is based on a priori SNR estimation. A priori SNR estimation, which is a key parameter in MMSE-STSA estimator, was performed by using ''decision directed method.'' The ''decision directed method'' provides a trade off between noise reduction and signal distortion when correctly tuned. The experiments were conducted for various noise types. The results of proposed method were compared with those of other popular methods, Wiener estimation and MMSE-log spectral amplitude (MMSE-LSA) estimation in frequency domain. To test the performance of the proposed speech enhancement system, three objective quality measurement tests (SNR, segSNR and Itakura-Saito distance (ISd)) were conducted for various noise types and SNRs. Experimental results and objective quality measurement test results proved the performance of proposed speech enhancement system. The proposed speech enhancement system provided sufficient noise reduction and good intelligibility and perceptual quality, without causing considerable signal distortion and musical background noise. <s> BIB004
Most of the speech enhancement algorithms are applied in the frequency domain, using short-time Fourier transform (STFT), which allows analyzing nonstationary speech signals. STFT provides a compromise between time resolution and frequency resolution. However, once the frame length is chosen, the time resolution is the same for all frequency components. Some of the speech enhancement algorithms are developed using wavelet transform, which provides more flexible time-frequency representation of speech BIB004 . One popular technique for wavelet-based signal enhancement is the wavelet shrinkage algorithm BIB001 . Wavelet shrinkage is a simple denoising method based on the thresholding of the wavelet coefficients. The estimated threshold defines the limit between the wavelet coefficients of the noise and those of the target signal. However, it is not always possible to separate the components corresponding to the target signal from those of noise by simple thresholding. For noisy speech, energies of unvoiced segments are comparable to those of noise. Applying thresholding uniformly to all wavelet coefficients not only suppresses additional noise but also some speech components, like unvoiced ones BIB004 . Consequently, the perceptual quality of the filtered speech is affected. Therefore, the wavelet transform combined with other signal processing tools like Wiener filtering in the wavelet domain and wavelet filter bank have been proposed for speech enhancement BIB002 . More recently, a number of attempts have been made to use perceptually motivated wavelet decompositions, coupled with various thresholding and estimation techniques BIB003 .