International Journal of Advanced Computer Engineering and Communication Technology (IJACECT) _______________________________________________________________________________________________
Medical Image Compression Based on Daubechies Wavelet, Global Thresholding and Huffman Encoding Algorithm
1D.Ravichandran, 2Ramesh Nimmatoori, 3Ashwin Dhivakar MR
1Dept of CSE, ATRI, HYDERABAD
2Aurora Group of Colleges, HYDERABAD
3Dept of CSE, JNU, JAIPUR
Abstract- Due to the advent of medical image modalities such as X-ray angiography, CT imaging, MRI, ultrasound and digital video, a large volume of image data is being generated in hospitals and medical organizations nowadays. One of the hurdles faced by the health care institutions is limited network bandwidth to access, transfer and share these medical images for the teleconsultation, telediagnosis and telemedicine for the primary diagnostic purposes. Image compression gives the best options for reducing the cost effective delivery of medical images across the globe. Wavelet based image compression is the fundamental block in JPEG-2000 standard due to its good characteristics and multiresolution. The aim of this study is to identify the correlation between level of decomposition of the wavelet filter and quality of the reconstructed image. To investigate this, the most popularly referred to in the literature Daubechies wavelet (db2) filter is used for multilevel decomposition on a selected set of medical images and then global thresholding is applied for quantization. The quantized values are encoded through Huffman variable entropy coding technique. The results of this investigation are presented in this paper. The simulation results show that the proposed algorithm gives the better performance and useful for the developers for identifying the right or most appropriate level of decomposition of wavelet filter for medical image compression.
Keywords - Medical Image Compression, Daubechies Wavelet, Global Thresholding, Huffman Encoding
I. INTRODUCTION
It is well known that data compression is one of the successful, inevitable and predominant research areas in the field of image processing and that the wavelet transform has appeared as a pioneering and innovative technology[1]-[4]. Wavelet transforms have received significant attention in diverse areas of engineering and scientific applications such as signal and image processing, audio and video compression, antenna and wave propagation, pattern recognition and computer vision, detection of aircrafts and submarines and other medical image technology [2]-[3].
A wavelet means a small wave and is an oscillation that decays quickly. Wavelet filter is used to decompose a
complex information signal into elementary forms at different positions and scales. The wavelet transform is established and developed on the basis of Fourier transform [5]. Although Fourier transform is a powerful tool for analyzing the components of a stationary signal but it is failed for analyzing the non-stationary signal [6]. Wavelet transform is superior in all aspects and also supports multiresolution analysis (MRA) of a signal [5],[8],[9],[12]. Image data compression is a technique that is concerned with the reduction of number of bits required to store and transmit image without appreciable loss of information [3].
A typical wavelet based image coder consists of three major parts: a wavelet filter, a quantizer and an entropy coder (Fig 1a & 1b). The wavelet filter bank decomposes the image into wavelet coefficients [9]. The quantizer then quantizes the wavelet coefficients. The entropy coder produces an output bit stream and then encodes these wavelet coefficients. Although the overall performance of the image compression depends on all three parts of the coder, the choice of wavelet filter decomposition will ultimately affect the performance of the coder. If the wavelet filter performance is poor, it will not maintain the picture quality [12]-[14].
Fig 1(a) Coding Section
Fig 1(b) Decoding Section
Figure (1a & 1b) The process of Image compression based on wavelet Transform
In theory, a wavelet based compression techniques can decompose the image to any desired level but in practice it is not feasible due to high computational time [14].
Motivation of this research work is to investigate the
trade-off between the number of levels of image decomposition and quality of the reconstructed image.
The simulation work was conducted on a selected set of medical images of different modalities. The qualitative and quantitative results of these simulations are presented in this paper.
The remainder of this paper is organized as follows.
Section II deals with the Discrete Wavelet Transform (DWT) and its salient features for image compression.
Section III highlights the importance of hard and soft thresholding for image compression. Section IV focuses on the research methodology and working environment of the proposed algorithm. Section V gives in detail about experimental results and discussions. The conclusion and future direction of the work is summarized in Section VI.
II. DISCRETE WAVELET TRANSFORM
Discrete Wavelet Transform (DWT) is one of the transform based coding techniques which uses a reversible and linear mathematical transform in order to map the pixel values into a set of coefficients. The main feature of DWT is multiscale, invertible and orthogonal [6],[8]. An image is a two dimensional array of M rows and N columns of pixel elements. Discrete wavelet transform (DWT) is used to transform the image from its spatial domain into its frequency domain.
(A) Daubechies Wavelet filter
Daubechies wavelet filter is the fundamental wavelet, biorthogonal and symmetric [5],[12]. It is also widely used in solving a broad range of problems such as similarity properties of a signal, fractal problems and signal discontinuities [8]. They have maximal number of vanishing moments and hence they can represent high degree of polynomial functions [9].
(B) Number of Decompositions
The quality of compressed image depends on the number of decomposition [12]. Decomposition level selection of wavelet transform is also an important task because computational complexity depends on it [13].
The optimal number of decomposition gives the highest PSNR values in the wide range of compression ratios for a given filter order [14].
III THRESHOLDING
Thresholding is a denoising process which is one of the most commonly used quantization techniques for signal and image processing [7]. Threshold comprises the reduction or complete removal of selected wavelet coefficients in order to separate out the noise within the signal. In wavelet based denoising techniques, the coefficients are distinguished between significant coefficients which consists of important signal components and insignificant coefficients which are likely due to noise or redundancy of the inter-pixel elements of the image. Wavelet shrinkage (compression and denoising) is usually performed using one of the two
dominant thresholding techniques such as hard thresholding and soft thresholding.
(A) Hard thresholding
The hard threshold filtering technique is also called as global thresholding as it does the 'keep or kill' method. It removes the coefficients below a threshold value determined by the noise variance. Values of pixels which are less than threshold are made to zero and otherwise keep as it is. Hard thresholding method can be represented in mathematically as follows:
(B) Soft thresholding
The soft thresholding technique is applied to shrink the wavelet coefficients above or below the threshold value.
Values of pixels which are less than threshold are made to zero as in the case of hard thresholding technique but the values which are greater than the threshold will get subtracted from the threshold values. Soft thresholding method can be represented in mathematically as follows:
Selecting the right or appropriate threshold value can also be difficult due to a small threshold value creates a noisy result near the input, while a large threshold value introduces bias. The optimal threshold is somewhat in between.
(C) Huffman Entropy coding
Entropy coding is the last stage in the JPEG/JPEG- 2000/JPEG-LS procedure.The JPEG proposal specifies two entropy coding methods: Huffman coding and Arithmetic coding. Huffman variable entropy coder has become not only a de facto standard but also an efficient, easy and fast coding method. The main drawback of arithmetic coding is that it tends to be slow and difficult to implement [10]. Huffman coding used in image compression is based on the frequency of occurrences of the pixels in an image instead of symbols in a message. The pixels that occur frequently are encoded with a lower number of bits. A Huffman code table and the encoded pixels must be transmitted so that decoding can be carried out [11].
IV.RESEARCH METHODOLOGY AND WORKING ENVIRONMENT
The research methodology of the proposed wavelet image compression algorithm (Fig 2) is summarized as follows:
1. Load Image in MATLAB using Image Acquisition
2. Convert the image from RGB to grey scale
3. Draw histogram probability reduction function on grey scale components.
4. Apply Forward Discrete Wavelet Transform (FDWT) using Daubechies (db2) wavelet filter and set the number of levels of decomposition.
5. Apply Image quantization through global thresholding and select the threshold values.
6. Calculate probability index for each unique quantity.
7. Calculate unique binary code of Huffman code for each unique symbol.
8. Apply Huffman compression using Huffman tree.
9. At the receiving end, perform an inverse DWT of the data received from step-8
10. Calculate CR and PSNR and MSE.
Fig 2 Flow Diagram of the proposed method
Fig 3 Wavelet Decomposition Level
In wavelet transform, decomposition of an image consists of two parts, one is lower frequency or approximation of an image (scaling function) and another is higher frequency or detailed part of an image (wavelet function). At every level of decomposition, the four sub-images are obtained, the approximation (LL), the vertical detail (LH), the horizontal detail (HL), and the diagonal detail (HH). Then all the coefficients are discarded, except the LL coefficients that are transformed into the second level (Fig 3).
V. EXPERIMENTAL RESULTS AND DISCUSSIONS
The proposed method is implemented in the MATLAB (2014 a) and the operating system used here is windows OS 7. The MATLAB wavelet toolbox function 'wavedec2' is used to perform wavelet transform. The image is decomposed into its coefficients using the 'wavedec2' function. The decomposition depends on the type of wavelet and the level of decomposition (Fig 4 and Fig 5).
Fig. 4 Original Image and its histogram
Fig.5 Reconstructed Image and its histogram The performance of the image coder is evaluated based on the PSNR, MSE and CR and given in the following tables (Table 1 to Table 4). In this experiment, we have done compression and reconstruction of a selected set of medical images from different modalities by using the Daubechies (db2) wavelet filter at four different decomposition levels which are level 1, level 2, level 3, and level 5. All these images are grey scale image with depth 8 bits per pixel.
Threshold Mean Square Error (MSE)
PSNR in db
Compressi on Ratio (CR)
0.5 0.00716 69.581 21.099
2 0.123 57.2307 29.181
5 1.253 47.151 38.208
10 7.065 39.6399 48.511
15 17.83 35.6188 55.367
20 32.25 33.0459 60.033
Table 1. Performance Results of Compression Scheme based on DWT Decomposition Level : 1
Threshold Mean Square Error(MSE)
PSNR in db
Compressi on Ratio (CR)
0.5 0.00888 68.6482 24.04
2 0.1578 56.1492 34.538
5 1.501 46.3669 45.322
10 8.26 38.9613 57.216
15 21.03 34.9019 34.9019
20 39.07 32.2129 71.045
Table – 2 Performance Results of Compression Scheme based on DWT Decomposition Level : 2
Threshold Mean Square Error (MSE)
PSNR in db
Compression Ratio (CR)
0.5 0.00906 68.5605 24.215
2 0.1668 55.9082 35.282
5 1.559 46.2018 46.55
10 8.496 38.8385 58.769
15 21.63 34.781 67.039
20 40.17 32.0917 72.946
Table – 3 Performance Results of Compression Scheme based on DWT Decomposition Level : 3 Threshold Mean
Square Error (MSE)
PSNR in db
Compression Ratio (CR)
0.5 0.00908 68.5514 24.14
2 0.1675 55.8902 35.261
5 1.568 46.1761 46.592
10 8.533 38.8196 58.846
15 21.72 34.7622 67.137
20 40.37 32.0707 73.066
Table – 4 Performance Results of Compression Scheme based on DWT Decomposition Level : 5 The following figures (Fig 6- Fig 11) show comparison of reconstructed X-ray image (256 x256 pixels, 8 bit pixel) for 1,2,3,5 levels of decompositions at bit rate 1 bpp.
Fig 6 Compression Ratio vs PSNR
The optimal number of decompositions depends on filter order. Figure 4 shows PSNR values for different filter orders. It can be seen that as the number of decompositions increases, PSNR is increased up to some number of decompositions. Beyond that, increasing the number of decompositions has a negative effect. Higher filter order does not imply better image quality because of the filter length, which becomes the limiting factor
Wavelet Filter : Daubechies (db2), Image Name : MRI Head, Format : jpeg/jpg
Image size : 214 x 234
for decomposition. Decisions about the filter order and number of decompositions are a matter of compromise [12]-[14]
A suitable number of decompositions should be determined by means of image quality and less computational operation.
Fig 7 Threshold vs Compression Ratio (CR)
Fig 8 Threshold vs Mean Square Error (MSE)
Fig 9 Threshold vs PSNR
Fig 10 Compression Ratio (CR) vs Mean Square Error (MSE)
Fig 11 PSNR vs Mean Square Error (MSE)
VI. CONCLUSIONS AND FUTURE WORK
In this proposed paper, we have implemented a hybrid algorithm for medical image compression based on Daubechies wavelet, global thresholding and Huffman encoding. In our experiment, we have investigated the trade-off between quality of the reconstructed image and number of decomposition levels of the wavelet filter. The performance of the image coder is evaluated based on the PSNR obtained. In earlier research work concluded that the coding efficiency is contributed by the first five levels of decomposition of the wavelet filter [12]. Our study results also proved its consistency that quality of the coder is not significantly changed from the third level to the fifth level of wavelet decomposition.
Based on the above investigation, we comprehend that it would be reasonable to use the first three levels of decomposition for better performance of image compression on medical images for time limited computational complexity. It is also observed that adaptive decomposition is required to achieve balance between image quality and complexity of computations.
The future direction of the research work will be to study on performance of the coder based on the image statistics and image features.
ACKNOWLEDGMENT
The authors would like to express their gratitude to the management of Aurora group of colleges, Hyderabad where this work was performed and thank Dr Suresh Babu, Professor in CSE, for helpful discussions during the course of this work.
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