Modified noncausal smoothing filter and low rank matrix approximation for noise reduction
Teeradache Viangteeravat, Don Mitchell Wilkes · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2010
Removing noise in real time has become a high priority for analyzing data corrupted by additive noise. It is a major problem in various applications such as speech, image processing and real time multimedia services. Although considerable interest has arisen in recent years regarding wavelets as a new transform technique for many applications, the linear adaptive decomposition transform (LDT) has yielded results superior to the discrete wavelet transform (DWT) not only in terms of using a lower number of decomposition levels but also achieving a smaller percentage normalized approximation error in the reconstructed signal. In this paper, a novel noise reduction method, based on a modified noncausal smoothing filter and low rank approximation based upon the sum of minimum magnitude error criterion (i.e., l1 norm) is introduced that distinguishes itself from these other methods. The performance of the proposed approach was evaluated based on one dimensional data sets as well as speech samples. It is demonstrated that the approach yields very promising results on the test signals of the Donoho and Johnstone as well as to speech signals.