Arithmetic Coding for Images

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25 December 2021

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Keywords: data compression, arithmetic coding, Wavelet-based algorithms Abstract. Data compression is a standard requirement for a lot of the computerized functions. There are number of knowledge compression algorithms, that are dedicated to compress completely different knowledge codecs. Even for a single information kind there are variety of totally different compression algorithms, which use completely different approaches.

This paper examines lossless knowledge compression algorithm “Arithmetic Coding” In this method, a code word just isn’t used to represent a logo of the text. Instead it uses a fraction to represent the complete supply message.

The prevalence chances and the cumulative possibilities of a set of symbols within the source message are taken under consideration. The cumulative chance vary is used in both compression and decompression processes. In the encoding process, the cumulative possibilities are calculated and the vary is created in the beginning.

While reading the supply character by character, the corresponding range of the character throughout the cumulative likelihood vary is selected. Then the chosen vary is divided into sub elements in accordance with the possibilities of the alphabet.

Then the next character is read and the corresponding sub range is selected. In this fashion, characters are read repeatedly till the end of the message is encountered.

Finally a number must be taken from the final sub vary as the output of the encoding process. This might be a fraction in that sub range. Therefore, the complete source message could be represented using a fraction. To decode the encoded message, the variety of characters of the source message and the probability/frequency distribution are needed.


Compression is the artwork of representing the information in a compact type rather than its original or uncompressed form. This may be very useful when processing, storing or transferring a huge file, which wants plenty of assets. If the algorithms used to encrypt works correctly, there should be a major difference between the original file and the compressed file. Compression may be classified as both lossy or lossless. Lossless compression techniques reconstruct the original information from the compressed file with none lack of information. Some of the principle methods in use are the Huffman Coding, Run Length Encoding, Arithmetic Encoding and Dictionary Based Encoding.

Image compression is the application of information compression on digital photographs. In effect, the target is to scale back redundancy of the image information in order to have the ability to retailer or transmit information in an environment friendly kind. Lossy wavelet based compression is especially suitable for pure photographs similar to photos in purposes where minor lack of fidelity is appropriate to realize a considerable discount in bit fee.

Smooth areas of the picture are efficiently represented with a few low-frequency wavelet coefficients, whereas important edge features are represented with a couple of high-frequency coefficients, localized around the edge. The majority of the knowledge is localized in low frequency filters whereas the high frequency filters are sparse. Wavelet-based algorithms have been adopted by authorities companies as a regular methodology for coding fingerprint images, and are considered within the JPEG2000 standardization exercise.

Figure 1Image compression/decompression system
We applied wavelet with integer lifting
The integer wavelet with lifting has three steps:

Separation step: Separating the main sign to odd and even components. Lifting step: we apply the prediction filters and replace even and odd indicators. Normalization step
The subsequent step is implementing the coder/decoder items shown in Figure 1. For our coder and decoder we now have chosen Arithmetic coding over Huffman code.. We used C++ for our compressor and de-compressor. The enter to the compressor techniques is a 256 gray scale bitmap file. In compressor, first, we learn the bitmap matrix and pass it to wavelet module. The integer to integer wavelet is applied to the matrix in two dimensions each horizontally and vertically. The arithmetic encoder, code the remodeled 2-D wavelet and generates the compressed file.

In de-compressor, the compressed file is then passed to the decoder for decompression. The inverse integer wavelet remodel is then utilized to generate the bitmap matrix. The ultimate bitmap image is generated which is the retrieved picture. Description. Our system has the following classes:

-Wavelet class: The wavelet class is for integer to integer forward and inverse wavelet transforms. It does the forward integer wavelet transform each in 1 dimension and also 2- D on matrix which corresponds to the picture column and row pixels. In the inverse wavelet transform, we reverse all forward course of. It does each 1-D and 2-D wavelet rework.

-Image class: This class reads and write picture from the 256 grey scale bitmap file. It reads the image before the rework and compression and likewise regenerates the .bmp file after the decompression and inverse wavelet rework.

-Arithmetic Coder class: In arithmetic coding, we separated the source modeling from entropy coding. For coding functions the only information wanted for modeling an information source is its number of knowledge symbols, and the probability of each image. During the precise coding process what’s used is information that’s computed from the chances. The arithmetic encoder does the coding and the decoder generates the original decoded symbols.

-Codec class: It instantiates image, wavelet, Arithmetic coder and compress and decompress image utilizing wavelet and arithmetic coding.
-Utilities class: Utilities are some utility functions for observing the outputs, doing take a look at and debugging.
-Matrix class: This is a class for data matrix manipulation and matrix processing. Algorithm Steps.

1. We begin with a current interval” [L;H) initialized to [0; 1). 2. For each image of the file, we perform two steps :
(a) We subdivide the present interval into subintervals, one for every potential alphabet symbol. The size of a symbol’s subinterval is proportional to the estimated probability that the image would be the next image in the file, in accordance with the model of the input.

(b) We select the subinterval corresponding to the image that actually happens next within the file, and make it the new current interval.
3. We output enough bits to distinguish the final present interval from all other potential last intervals.


The following is a pattern of our 2-level wavelet remodel applied on a 512 x 512 gray scale bitmap picture.

Figure 3. Results from applying 2 levels of wavelet on a 512 x 512 bitmap

The thought behind wavelet transform is expressed in Fig.three. Most of the image data is within the low frequency filters. High frequency filters only characterize the nice particulars. For the lossy compression, the concept is to ignore the excessive degree transforms and regenerate your signal using your low frequency filters. Below, we present our results from applying our compression to completely different sizes.



[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. eighty two, no.6, June 1994.

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"Arithmetic Coding for Images" StudyScroll, 25 December 2021,

StudyScroll. (2021). Arithmetic Coding for Images [Online]. Available at: [Accessed: 19 August, 2022]

"Arithmetic Coding for Images" StudyScroll, Dec 25, 2021. Accessed Aug 19, 2022.

"Arithmetic Coding for Images" StudyScroll, Dec 25, 2021.

"Arithmetic Coding for Images" StudyScroll, 25-Dec-2021. [Online]. Available: [Accessed: 19-Aug-2022]

StudyScroll. (2021). Arithmetic Coding for Images. [Online]. Available at: [Accessed: 19-Aug-2022]

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