【摘要】 针对低秩约束和稀疏矩阵分解(constrained low-rank and sparse matrix decomposition, CLSMD)方法中硬阈值可能导致降噪后的语音信号分量丢失或出现孤立噪声问题，提出了一种自适应秩约束逆矩阵近似(adaptive rank constrained inverse matrix approximation, ARCIMA)分解方法。该方法首先采用能量阈值法初步估计低秩矩阵秩值，然后从语音信号子空间矩阵的结构特性出发，采用修正双边随机投影(modified bilateral random projections, MBRP)方法求解代表纯净语音信号的低秩矩阵，降低使用SVD方法的计算量，并通过Tikhonov正则化优化方法改善迭代求解过程中解的病态性。实验结果表明，该方法相比经典方法在多种噪声环境下取得了更好的PESQ得分，并且增强语音的时域波形也更接近原始信号的波形。该方法去噪性能在低信噪比噪声条件下具有优势。更多还原

【Abstract】 This paper proposed a new matrix decomposition method ARCIMA to address issues in the CLSMD approach, where hard thresholding could lead to loss of speech signal components or isolated noise problems. Initially, the energy thres-hold method estimated the rank of the low-rank matrix. Then, considering the structural characteristics of the speech signal subspace matrix, the MBRP method solved the low-rank matrix representing the clean speech signal, reducing the computational load compared to the SVD method. Tikhonov regularization optimized the solution’s stability during iterative solving. Experimental results show that this method achieves better PESQ scores in various noisy environments compared to classical methods, and the enhanced speech waveform is closer to the original speech waveform. The method demonstrates superior denoising performance under low signal-to-noise ratio conditions.更多还原