启发式联合PCD快速降噪算法

基于稀疏冗余表示，并行坐标下降(PCD)是最优秀的降噪算法之一。然而在音频信号处理中，当分割的帧数很大时，PCD的计算负担加重，造成运行时间剧增。该文基于联合稀疏表示(JSR)和同时稀疏近似(SSA)，建立一种新的时域框架，并提出了一种启发式联合PCD算法(Joint-PCD)。在该框架中，每个音频帧作为一个列向量生成信号矩阵；利用超完备字典，Joint-PCD同步(同时)对信号矩阵降噪，提高了算法的运行效率，减小了运行时间。仿真结果表明:Joint-PCD算法不仅与PCD具有几乎相同的降噪性能，且把PCD算法的降噪速度提高了约5倍，极大地改进了PCD算法的收敛性能。

Novel Heuristic Joint PCD Fast Denoising Algorithm

Based on sparse and redundant representation, parallel coordinate descent (PCD) is one of the best denoising algorithms. In audio signal processing, however, when the number of segmented frames is large, the computational burden is heavy. Processing each frame separately with the PCD algorithm causes a dramatic increase in time cost. Therefore, this paper proposes a new time-domain framework and a heuristic joint PCD (called joint-PCD) algorithm based on joint sparse representation (JSR) and simultaneous sparse approximation (SSA). In this framework, each audio frame is used as a column vector to generate a signal matrix. Utilizing an over-complete dictionary, joint-PCD is used to synchronously (simultaneously) denoise a signal matrix (instead of an audio frame), which greatly improves the efficiency of the algorithm and reduces the burden of running time. The simulation results show that the joint-PCD algorithm not only has almost the same and excellent denoising performance with PCD, but also increases the denoising speed of PCD by about five times, which greatly improves the convergence performance of the PCD algorithm.