Optimal Wavelet Basis for Image Compression

Unlike Fourier basis which constitutes fixed sine and cosine waves; the Wavelet Transform has infinite basis functions. The choice of good basis is application dependent. Statistical parameters of the image are dynamic and differ from image to image. A moment vector of natural image will be different from the moment vector of synthetic image. Similarly the edges in natural image have structural variations and will be reflected in its subbands whereas synthetic images of thin lines, contours or geometric shapes have least correlation amongst the subbands. Therefore, good basis is a function of image statistical parameters. In this work an effort has been made to implement different classical Orthogonal, Bi-orthogonal and Symmetric wavelets on different images with a view to evaluate good wavelet basis for image compression. This paper discusses the effects of various wavelet functions on different images, zeros and retained energy after thresholding the wavelet coefficients of the decomposed image along with Peak Signal to Noise Ratio of the synthesized image. In order to achieve better compression system, the appropriate wavelet basis are required to be chosen depending upon type of the input image. Index terms —Wavelets, Optimal basis, image compression.