# Arithmetic Coding for Images

Topics: Data compression, Lossless data compression, Huffman coding Pages: 5 (1255 words) Published: January 5, 2013
Arithmetic Coding For Images

1. Sanjay Bellani, 2. Shikha Bhagwanani

1. Plot No.421(a),Ward 2b . Adipur (Kutch) INDIA

2. Plot No.107,Ward 3b. Adipur(Kutch) INDIA

a. Innocentboy.sanju@yahoo.com, b. Shikha.bhagwanani@gmail.com

Keywords: data compression, arithmetic coding, Wavelet-based algorithms Abstract. Data compression is a common requirement for most of the computerized applications. There are number of data compression algorithms, which are dedicated to compress different data formats. Even for a single data type there are number of different compression algorithms, which use different approaches.

This paper examines lossless data compression algorithm “Arithmetic Coding” In this method, a code word is not used to represent a symbol of the text. Instead it uses a fraction to represent the entire source message. The occurrence probabilities and the cumulative probabilities of a set of symbols in the source message are taken into account. The cumulative probability range is used in both compression and decompression processes. In the encoding process, the cumulative probabilities are calculated and the range is created in the beginning.

While reading the source character by character, the corresponding range of the character within the cumulative probability range is selected. Then the selected range is divided into sub parts according to the probabilities of the alphabet. Then the next character is read and the corresponding sub range is selected. In this way, characters are read repeatedly until the end of the message is encountered.

Finally a number should be taken from the final sub range as the output of the encoding process. This will be a fraction in that sub range. Therefore, the entire source message can be represented using a fraction. To decode the encoded message, the number of characters of the source message and the probability/frequency distribution are needed.

Introduction. Compression is the art of representing the information in a compact form rather than its original or uncompressed form. This is very useful when processing, storing or transferring a huge file, which needs lots of resources. If the algorithms used to encrypt works properly, there should be a significant difference between the original file and the compressed file. Compression can be classified as either lossy or lossless. Lossless compression techniques reconstruct the original data from the compressed file without any loss of data. Some of the main techniques in use are the Huffman Coding, Run Length Encoding, Arithmetic Encoding and Dictionary Based Encoding.

Image compression is the application of data compression on digital images. In effect, the objective is to reduce redundancy of the image data in order to be able to store or transmit data in an efficient form. Lossy wavelet based compression is especially suitable for natural images such as photos in applications where minor loss of fidelity is acceptable to achieve a substantial reduction in bit rate. Smooth areas of the image are efficiently represented with a few low-frequency wavelet coefficients, while important edge features are represented with a few high-frequency coefficients, localized around the edge. The majority of the information is localized in low frequency filters while the high frequency filters are sparse. Wavelet-based algorithms have been adopted by government agencies as a standard method for coding fingerprint images, and are considered in the JPEG2000 standardization activity.

Figure 1.Image compression/decompression system
We implemented wavelet with integer lifting
The integer wavelet with lifting has three steps:
I) Separation step: Separating the main signal to odd and even parts. II) Lifting step: we apply the prediction filters and update even and odd signals. III) Normalization step
The next step is implementing the coder/decoder units shown in Figure 1. For our coder and decoder we have chosen...

References: [1] Amir Said,Introduction to Arithmetic Coding Theory and Practice, Hewlett-Packard Laboratories Report, HPL-2004-76, Palo Alto, CA, April 2004.
[2] C. Sidney Burrus, Ramesh A. Gopinath, Haitato, "Introduction to Wavelets and Wavelet Transforms, Aprimer," Prentice-Hall, New Jersey, 1998.
[3] M. D. Adams and F. Kossentini, "Reversible Integer-to-Integer Wavelet Transforms for Image Compression: Performance Evaluation and Analysis," IEEE Trans. on Image Processing, vol. 9, no. 6, pp. 1010-1024, Jun. 2000.
[4] Paul G. Howard AND Jeffrey Scott Vitter, "Arithmetic Coding for Data Compression", Proceedings of the IEEE, vol. 82, no.6, June 1994.