Lossless Image Decomposition And Reconstruction Using Haar Wavelets In Matlab For Ecet Students

A method for introducing the topic of lossless image decomposition and reconstruction to ECET students is presented. The definition and frequency selective properties of the Haar wavelet is introduced. In addition, the application of Haar wavelets to the decomposition and reconstruction of a 1-dimensional signal is explained and serves as a stepping stone to discussing the application to digital images. Introduction In the past few years, the authors reported their efforts of enhancing students’ learning by utilizing a systems approach [1] [4]. These methods focus on the functionality of system blocks to improve students’ understanding of system performance parameters. Positive results have been observed in strengthening students knowledge development on certain subjects. The systems approach has been applied to the development of engineering algorithms. In the Spring semester of 2005, we initiated a project in a Digital Signal Processing class to implement a Matlab R © algorithm that would produce lossless decomposition and reconstruction of a digital image using wavelets. The reason we chose this topic is twofold. First, the project allows the student to subdivide two complicated processes into managable system blocks. This training will be helpful when the ECET student graduates and takes on the challenges of the engineering community. Second, the project permits testing and detection of algorithm errors at the output of each system block. This is due to the fact that decomposition and reconstruction are identically reverse processes, which provide the capability for comparison of the output at each stage of decomposition with that of reconstruction. Lastly, the use of images allows the student to visualize the effects of each system block, and thereby gain an understanding of the function of each block. This article reports on some results in introducing this topic into a Digital Signal Processing class. Upon completion, this experimental design is intended to be used in our Microcontroller course for hardware implementation. P ge 11903.2 Haar Wavelets The basic Haar wavelets are a set of low and high pass digital filters that can be used for lossless decomposition and reconstruction [5]. The low pass Haar wavelet is