Frames and their applications in signal denoising

One classical way to solve signal denoising is shrinkage of a representation of the data in a wavelet basis. Because the disadvantage of demanding high order vanishing moments in applications, we have to consider frames. In the paper we first consider the main idea of denoising of a signal using frames, and then discuss the selection problem of frames in applications. We reveal that the tight wavelet frames derived from MRA constructed by Ron and Shen are easiest to use. Following the orthogonal wavelet shrinkage method of Donoho and Johnstone, we can set to zero all wavelet frame coefficients with respect to a reasonable threshold, and then restore the signal with the new coefficients. © 2014 Binary Information Press.