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An analysis of color image compression using Golomb-rice algorithm.


Images are of two types. One is gray scale Image and another one is color image. On comparison with the gray scale image, more minute details can be observed in the color image. A high performance lossless color image compression and decompression techniques (Hallnor et al, 2005 and Roy et al, 2001) is used to reduce both memory requirements and bandwidth. The Differential data conversion using Raster file and Golomb Rice Algorithm are commonly used compression and decompression techniques.

In the existing method, image of size m x n is taken as an input and it is converted into differential data by using DDPCM (Differential Pulse Code Modulation) (Morein, 2000) which will produce image of size m x n-1. Then the previous output has been given as an input to the compression block. In the compression block the image is compressed and it will sent to the GR encoder block we can check whether the image is compressed or not by using v bit. If v bit is 0, then the image is not compressed and if v bit is 1, means the image is compressed based on v bit only, we can encode the image by using GR encoder, based on the code word, quotient and remainder values are obtained. The output of the GR encoder has been given as an input to the decoder block, in the decoder block the encoded image can be decoded by using GR decoder. Then decoded image is decompressed by using inverse DDPCM and then original image has been obtained. The compressed memory architecture should utilize a loss-less compression algorithm because the original image should be reconstructed from the compressed one. In addition, a hardware-based rather than a software- based compression methodology (Tsai et al., 2010) is required in order to implement real-time features for data processing.

Lossless image compression (Denecker et al., 2002, Brooks et al., 2004, Chen et al, 2008 and Milward et al., 2004) has been addressed with Lempel-Ziv code (Ziv et al., 1978), Golomb- Rice code (Golomb, 1966), JPEGLS (Xiaowen et al., 2007), and CALIC (Wu et al., 1997). Most of these methodologies are software-based approaches targeting a high compression rate. They require complex hardware implementations to achieve sufficient performance of compression for color image data. In (Nakar et al., 2004), in order to address the performance penalty which software-based approaches usually accompany, the working sets are selectively compressed according to the program phase in which the changes are detected.

The compressed memory schemes used to improve the performance of embedded systems (Cheng et al., 2005) has been proposed. Operating system-based memory compression architecture is proposed to provide onthe-fly compression and decompression for embedded systems (Yang et al., 2007). Discrete Cosine Transform (Osorio et al., 2006) based memory compression techniques can be applied to the motion-estimation applications. Image compression hardware architecture based on Hadamard transform and Golomb-Rice coding (Lee, 2003) is proposed. In the techniques discussed earlier, it loses some data during the Hadamard transform and Golomb-Rice encoding. A new hardware-friendly adaptive decimation algorithm (Wu et al., 2010) can be utilized to achieve low bit rate and less image quality.


A. Block Diagram and Its Description:

The input image is compressed by using discrete wavelet transform. The output of the 2-Dimensional discrete wavelet transform is in the form of sub-windows of m x n arrays. Then the image is converted into differential data by using raster file conversion. By using Golomb-Rice algorithm differential data has been encoded to produce length and code word of the input image. Based on the length and code word obtained the encoded image has been

Decoded using Golomb-Rice algorithm. The decoded image has been decompressed using the inverse 2-D discrete wavelet transform. The output produced is similar to that of the input image.

B. Discrete Wavelet Transform:

Wavelet transform is used to determine both the time and the frequency components simultaneously. The different types of DWT are 1D DWT and 2D DWT. Among these we have utilized 2-dimensional DWT.

2-Dimensional DWT:

In 2-D DWT, the input data is passed through set of both low pass and high pass filter in two directions, both rows and columns. The outputs are then down sampled by 2 in each direction. Discrete wavelet transforms (DWT) for hierarchical signal analysis and decomposition are implemented through an iterative filtering and down sampling operation with low pass and high pass filter operations.

Output is obtained in set of four coefficients LL, HL, LH and HH. The first alphabet represents the transform in row whereas the second alphabet represents transform in column. The alphabet L means low pass signal and H means high pass signal. LH signal is a low pass signal in row and a high pass in column. Hence, LH signal contain horizontal elements. Similarly, HL and HH contains vertical and diagonal elements, respectively.

Raster File:

Raster file is used to convert the image into differential data. Raster graphics are digital images created or capture as a set of samples of a given space. A raster is a grid of X and Y coordinates on a display space. A raster image file identifies which of these coordinates to illuminate in monochrome or color values. The raster file is sometimes referred to as a bitmap because it contains information that is directly mapped to the display grid.

Golomb-Rice Coder:

The output obtained from 1-D DWT compression is converted into differential data by using raster file conversion. In the Golomb rice encoding the differential data has been encoded then the length has been generated. Based on the generated length the code word has been calculated based on the remainder and quotient bits. Then the code word calculated would be converted into unary code.

The unary code obtained from the GR encoding is converted into code word, based on the code word the compressed image has been decoded. The decoded image is applied as an input to 2-D IDWT.

A.2-Dimensional Inverse Discrete Wavelet Transform

In DWT reconstruction, input data can be achieved in multiple resolutions by decomposing the LL coefficient further for different levels as shown in Figure 3. In order to reconstruct the output data, the compressed data is up-sampled by a factor of 2. The signal is further passed through the same set of high pass and low pass filter in both rows and columns. The reconstructed image is obtained as a gray image because code word is in the form of 0's and 1's. Then it has been converted into color image by using suitable matlab commands.

B. Golomb-Rice Algorithm:

Golomb coding is a lossless data compression method using a family of data compression codes invented by Solomon W. Golomb in the 1960s. Alphabets following a geometric distribution will have a Golomb code as an optimal prefix code.

Rice coding (invented by Robert F. Rice) denotes using a subset of the family of Golomb codes to produce a simpler (but possibly suboptimal) prefix code; Rice used this in an adaptive coding scheme, although "Rice coding" can refer to either that scheme or merely using that subset of Golomb codes.

Unary Code:

The simplest code for this situation is the unary code. The unary code for a positive integer n is simply n 1s followed by a 0. Thus, the code for 4 is 11110, and the code for 7 is 11111110.


The software implementation of the proposed Golomb-Rice algorithms is performed in MATLAB. PSNR & compression ratio has been determined and tabulated for simulated images. Lena and man image were used as simulated images. We compared with other techniques and found to be advantageous in picture quality.


Image compression and decompression has been performed by using DWT, IDWT and GR coder. It can allow images to be compressed with a high compression ratio, while maintaining high security during the transmission process. Bandwidth and security issues are overcome simultaneously. The experimental results indicate that the reconstructed images are of satisfactory quality. The simulation results show that the compressed image is generally good enough to human perception. Image compression and encryption scheme provides better quality images in terms of PSNR and Compression Ratio. In future the proposed algorithm can be implemented in real time video streaming using FPGA hardware (Chen et al, 2007) implementation.


Article history:

Received 3 September 2014

Received in revised form 30 October 2014

Accepted 4 November 2014


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(1) G. Sekar, (2) Dr. S. Valarmathy, (3) Dr. S. Mary Praveena, (4) S. Sam Jaikumar, (5) S.B. Aneith Kumar

(1,4,5) Assistant Professor, ECE, Sri Ramakrishna Institute of Technology, Coimbatore, India

(2) Professor, ECE, BannariAmman Institute of Technology, Sathyamangalam, Erode, India

(3) Professor, ECE, Sri Ramakrishna Institute of Technology, Coimbatore, India

Corresponding Author: G. Sekar, Assistant Professor, Department of ECE, Sri Ramakrishna Institute of Technology, Coimbatore, India.


Table 1: Comparision Of Compression Ratio For Various Methods.


            DDPCM+GR CODING             1.52
           X-MATCH ALGORITHM            1.51
PROPOSED     DWT+GR CODING              1.90

Table 2: Comparison Of Memory Size Of Simulated Image.

Images        MSE        Original image size   Compressed image size

 Man     2.1791e + 004          297kb                  4.4kb
 Lena    1.5478e + 004          732kb                 14.1kb

Images   Reconstructed image size

 Man              17.6kb
 Lena             37.8kb

Table 3: Comparison Of PSNR With Resolution
Progressive Compression(RPC) Algorithm.

Images                             PSNR


 Man                34.7                 25.179
 Lena               36.2                 34.095
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Author:Sekar, G.; Valarmathy, S.; Praveena, S. Mary; Jaikumar, S. Sam; Kumar, S.B. Aneith
Publication:Advances in Natural and Applied Sciences
Article Type:Report
Geographic Code:9INDI
Date:Nov 1, 2014
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