AN FPGA IMPLEMENTATION OF A DENOISIG ALGORITHM BASED ON STATIONARY WAVELET PACKET TRANSFORN

Abstract

Scientific datasets are often contaminated with noi se, either because of the data acquisition and transmis sion processes, or because of naturally occurring phenomena such as at mospheric disturbances. A first pre-processing step in analyz ing such datasets is denoising, that is, estimating the signal of interest from the available noisy data. Wavelet transforms represent signals wi th a high degree of sparsity. This is the principle behind the non-line ar wavelet based signal denoising technique and is what distinguishes it fr om entire linear denoising techniques such as least squares. It is w ell known that the use of non-decimated (Stationary) Wavelet Transforms (SWT) gives a redundant representation of an input signal, which minimizes the artifacts in the reconstructed data. In this work the stationary wav elet basis and the Wavelet Packet Transform (WPT) method are exploited to develop a Stationary Wavelet Packet Transform (SWPT)-based de noising algorithm. The decomposition of noisy signals is performed wit h stationary wavelets according to the optimum decomposition tree structu re, determined through the WPT method. The thresholding is performed on the coefficients of the best tree, to make the denoisin g process more efficient. The performance of the denoising algorithm is asses sed in terms of the Mean Squared Error (MSE) as a measure of the qualit y of denoisign . The obtained simulation results indicate that the combi nation of the SWT and WPT achieves superior denoising than the applicatio n of each of them separately. The proposed SWPT-based denoising algo rithm is efficiently implemented on Xilinx Virtex Field Programmable Gat e Array (FPGA).