Introduction

Image compression is an important technique used to assist in data storage and transmission. The idea is to represent an image with a smaller amount of information while still being able to recover the original image. There are two types of compression, lossless and lossy. Lossless coding tries to take advantage of redundancies in the image data to reduce the data size of the image. The original image can be decompressed perfectly. Lossy compression allows for error between the original image and the decompressed image in order to achieve significant gains in the amount of compression. There are many methods to try to get greater compression ratios while maintaining a small amount of error. In this paper we will explore several methods of transform coding.

Transform coding takes the original image data into a new domain to try to take advantage of the properties of the transform. For instance, if the transform takes correlated image data into a domain where the data is uncorrelated, that might be an advantage for compression the image. We used the Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) to explore the gains of transform coding. The DCT exploits the energy compaction of the transform to put most of the image information in a small number of bits. Thus, the majority of bits can be quantized to smaller bit sizes in order to gain compression. The Haar DWT localizes sums and differences between adjacent to try to localize the edge information of an image and reduce the bits size of the majority of bits. A higher order Daubechies wavelet transform will try to localize the edges of an image as well.

Once the images were transformed into their new domain, we used three different types of bit allocation algorithms to take advantage of the domain properties. As stated above, the algorithms will assign more bits to the higher energy image components and less to the lower energy components. The individual methods we chose will be explained in sections , and .

The objective of this paper is to explore the three compression methods and compare their compression rates (in Bits Per Pixel) to the Picture Signal to Noise Ratio (PSNR) in order to see witch method has the best compression for a given error.