Sparse Blind Speech Deconvolution with Dynamic Range Regularization and Indicator Function

Abstract

Blind deconvolution is an ill-posed problem. To solve such a problem, prior information, such as, the sparseness of the source (i.e. input) signal or channel impulse responses, is usually adopted. In speech deconvolution, the source signal is not naturally sparse. However, the direct impulse and early reflections of the impulse responses of an acoustic system can be considered as sparse. In this paper, we exploit the channel sparsity and present an algorithm for speech deconvolution, where the dynamic range of the convolutive speech is also used as the prior information. In this algorithm, the estimation of the impulse response and the source signal is achieved by alternating between two steps, namely, the ℓ 1 regularized least squares optimization and a proximal operation. As demonstrated in our experiments, the proposed method provides superior performance for deconvolution of a sparse acoustic system, as compared with two state-of-the-art methods.

Sparse Blind Deconvolution with Nonconvex Optimization for Ultrasonic NDT Application

“…The regularization parameters and indicator functions of [12,29] are adjusted in this comparison. In the case of K = 3, L = 20, and n = 1000, offset and polarity reversal presents in the conventional fast deconvolution methods, such as MED [11] and LS [17]. The MED algorithm uses an inverse filter to solve sparse reflection sequence directly.…”

“…The running time is obtained by taking the average value from experiments, and the stopping criterion for iterative algorithms is set as x (k+1) − x (k) 1 ≤ 10 −3 . Although the deconvolution based on LS [17] is superior in speed, the cost is a large estimation error. MED-based methods [9][10][11] achieve relatively good sparse sequence estimation in less computing time.…”

“…When multiple input signals are present, finding sparse vectors in a subspace can be directly converted into blind calibration [15]. In order to improve the stability of initialization, 2 norm projection [16], least-squares (LS) [17], and pruned tree search [18] are proposed. Zhang [19] explored the influence of symmetric structure on the iterative solution and recovered the shift truncation over the kernel sphere.…”

Adaptive Operator-Based Spectral Deconvolution With the Levenberg-Marquardt Algorithm

“…where 2 α S acts as the regularization term [23][24][25][26][27][28][29][30][31] and resembles the well-known Tikhonov regularization, and α is the regularization parameter. The regularization parameter α is usually unknown and needs to be determined by special methods according to the practical problem.…”

Blind Speech Deconvolution via Pretrained Polynomial Dictionary and Sparse Representation

“…There are unlimited possible combinations of s and h which satisfy (1). To address this problem, prior information (such as sparsity of signals [13] [15] [16] or acoustic impulse responses [7]) is usually exploited to reduce the solution space for the estimation of s and h.…”