Image Compression using Haar and Modified Haar Wavelet Transform - Mohannad Abid Shehab Ahmed; Haithem Abd Al-Raheem Taha; Musab Tahseen Salah Aldeen (Tikrit Journal of Engineering Sciences, 2011)
Efficient image compression approaches can provide the best solutions to the recent growth of the data intensive and multimedia based applications. As presented in many papers the Haar matrix–based methods and wavelet analysis can be used in various areas of image processing such as edge detection, preserving, smoothing or filtering. In this paper, color image compression analysis and synthesis based on Haar and modified Haar is presented. The standard Haar wavelet transformation with N=2 is composed of a sequence of low-pass and high-pass filters, known as a filter bank, the vertical and horizontal Haar filters are composed to construct four 2-dimensional filters, such filters applied directly to the image to speed up the implementation of the Haar wavelet transform. Modified Haar technique is studied and implemented for odd based numbers i.e. (N=3 & N=5) to generate many solution sets, these sets are tested using the energy function or numerical method to get the optimum one. The Haar transform is simple, efficient in memory usage due to high zero value spread (it can use sparse principle), and exactly reversible without the edge effects as compared to DCT (Discrete Cosine Transform). The implemented Matlab simulation results prove the effectiveness of DWT (Discrete Wave Transform) algorithms based on Haar and Modified Haar techniques in attaining an efficient compression ratio (C.R), achieving higher peak signal to noise ratio (PSNR), and the resulting images are of much smoother as compared to standard JPEG especially for high C.R. A comparison between standard JPEG, Haar, and Modified Haar techniques is done finally, which approves the highest capability of Modified Haar between others