“AN INVESTIGATION INTO THE MATHEMATICAL PROPERTIES OF WAVELET FRAME TRANSFORMATIONS AND THEIR APPLICATIONS IN SIGNAL AND IMAGE ANALYSIS”

Abstract

In recent years wavelet frame transformations have emerged as a significant mathematical tool and signal processing technique. Native orthogonal wavelets have the special feature of data representation at various resolutions and frequencies. In this paper, we provide an extensive treatment of the wavelet frame transformation including the necessary tools and properties. Furthermore, the study talks about its application in analysis of images and signals of wavelet frame transformation. Wavelet frames are an important aspect of frame theory and wavelet theory and relate to the more general development of frames in Hilbert spaces. Wavelet transform is useful because it represents a signal with level signals. In addition, It can do effective signal approximation in noise removal. The frame theory which developed a more general wavelet theory is where the study of frames started. The characterization of a wavelet frame with useful properties like tightness and compact support require the mining of results and techniques from other methods in mathematics, such as operator theory and harmonic analysis.