Formation of Wavelet - Transform Signals Taking Into Account Threshold Functions in the Digital Stream Compression Problem

Abstract

In order to reduce the digital stream, the problem of improving the quality of digital filtering based on Discrete Wavelet Transformation (DWT) was analyzed using different options for setting the threshold function and the choice of wavelet basis. Given the considerable interest in this problem and the numerous studies concerning the search for ways to optimize the suppression of interference present in signals and images, the topic continues to be relevant and important. For such tasks as image compression, operations in processing and synthesis of different signals, in the analysis of images of different nature, in reducing (compressing) large amounts of information, and to protect information is often used wavelet transform, implemented on the basis of mirror filters. For the formation of wavelet-transform signals taking into account the threshold functions in the problem of digital stream compression, a standard approach to solving the problem of signal purification from interference and random distortions using Daubechies wavelet and adjusting the signal decomposition coefficients based on wavelet functions using soft and rigid threshold task options. It is shown that the use of complex bases provides an advantage both in terms of threshold filtering error and in terms of reducing the risk of accidental distortion in the reconstruction of the useful signal by wavelet coefficients. Appropriate steps were taken for the test signal and experimental data. When using the threshold function, the large modulus (most significant) wavelet coefficients remain unchanged, and the small ones are reset to zero. The change in the amplitude of the recovered signal leads in the latter case to a decrease in the absolute values of all wavelet coefficients, including large modulo. For those applications where it is important to keep the amplitude characteristics constant, this approach is not suitable, but there are problems where it is more important to maintain the regularity of the signal than to accurately reproduce its amplitude. Rhis is the filtering of images from various obstacles, where the method of "soft" task of the threshold function is a widely used approach. When analyzing signals, the constant amplitude is also not always a mandatory requirement. An audio signal can be amplified after filtering, and pre-cleaning it from interference is more important than changing the amplitude characteristics. The use of complex wavelet transform allowed to obtain error reduction and lower threshold level when adjusting wavelet coefficients, and can be recommended for analysis of complex wavelet transform methods as an effective tool for cleaning signals and images of different nature for further research.