J. Comp. & Math. Sci. Vol. 1(7), 769-775 (2010)
Wavelet Based Medical Image Compression Using SPHIT AZIZ UR RAHAMAN MAKANDAR and K. KARIBASAPPA Research Scholar, Dept of Comp.Sc Singhania University, Pacheri Bari(R J), azizmakandar@gmail.com Dept of Comp.Sc & Engg, D S College of Engg, Bangalore-Karnataka (India), karibasappably@gmail.com ABSTRACT Current image coding systems use wavelet transform, which decompose the image into different levels, where the coefficients in each sub band are uncorrelated from coefficients of other sub bands. As a result the coefficients in each sub band can be quantized independently of coefficients in other sub bands with no significant loss in performance. But the coefficient in each sub band requires different amount of bit resources to obtain best coding performance. This results in different quantizer with each sub band having its own bit rate. This gives an issue to bit allocation under image processing. Hence sub band coding can be used for achieving high bit rate. The main purpose of this paper is to investigate the impact quality of orthogonal wavelet filter for Set Partitioning in Hierarchical Trees (SPHIT). The experimental results have been compared and qualitative analysis is done on the basis of time taken for compression and error after decompression for medical image. Keyword: Wavelet transforms; image compressions; SPHIT.
INTRODUCTION
based on DWT1–8 provide high coding efficiency for natural (smooth) images.
With the rapid expansion of computer technology, digital image processing place a great demand on efficient data storage and image content. Discrete Wavelet Transform (DWT) provides a multiresolution image representation and has become one of the most important tools in image analysis and coding over the last two decades. Image compression algorithms
In medical image compression, diagnosis is effective only when compression techniques preserve all the relevant information needed without any appreciable loss of information, in case with lossless compression. Lossy compression techniques are more efficient in terms of storage and transmission needs because of high compression ratio and the quality. In
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lossy compression, image characteristics are usually preserved in the coefficients of the domain space in to which the original image is transformed. The quality of the image after compression is very important and it must be within the tolerable limits which vary from image to image and method to method, hence the compression becomes more interesting as a part of qualitative analysis of different types of medical image compression techniques. SPHIT algorithm bases its efficiency in key concepts like: a) partial ordering of wavelet coefficients by magnitude, with transmission of order by a subset partitioning that is replicated at the decoder, b) ordered bit-plane transmission of refinement bits and c) exploitation of selfsimilarity of the image wavelet coefficients across different scales.23-24. Wavelet Compressions Wavelet based image compression has had great success as of recent due to the fact that its wavelet coding schemes combine excellent compression efficiency with the possibility of an embedded representation. In light of this, a few important coding schemes have emerged, they are Embedded Zerotree Wavelet (EZW) Encoding by Shapiro9 Set Partitioning in Hierarchical Trees (SPIHT) by Said and Pearlman18. Wavelets are mathematical functions that cut up data into different frequency components and then study each component with resolutions matched to its scale. They have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuation and sharp spikes. An important property of wavelet functions in image compression applications is compact support. In this paper, we consider Haar
Daubecbies wavelet19-22.
4,
Syamlet,
Biorthogonal
Medical Image Compression The compression of medical images has a great demand. The image for compression can be a single image or sequence of images. The medical community has been very reluctant to adopt lossless algorithms in clinical practice. However, the diagnostic data produced by hospitals has geometrically increased and a compression technique is needed that results with greater data reductions and hence transmission speed. In these cases, a lossless compression method that preserves the diagnostic information is needed.. Medical image like MR, CT, Ultrasound, X-Ray images are used for experiments A major design goal of any compression method is to obtain the best visual quality with lowest bit rate14-16. Lossless compression The tree structure of the 3 level wavelet decomposition Figure 1 shows, a sub-tree taking a coefficient in sub-band HH3 as the root node is demonstrated. If the coefficient (i, j) in sub-band HH3 is root node, the 4 coefficients in HH2 {2i+m, 2j+n}, her0≤m, n≤1, will be the child node, and the 16 coefficients in HH1 {4i+m, 4j+n}, here 0≤m, n≤3, will be the grandson node. There are 21 coefficients in a 3 level decomposition tree, and 20 coefficients are the grandson nodes of the root node. If a k (k=1, 2, 3, …) level wavelet decomposition is made, there will be grandson nodes belonging to the root node in sub-band HHk. K-1 ∑ 41 = 4/3 (4k-1-1) 1=1
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Aziz Ur Rahaman et al., J. Comp. & Math. Sci. Vol. 1(7), 769-775 (2010)
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The scanning order in the improved method begins from the high frequency coefficient of the last level rather than the low frequency coefficient. As Figure 1 shows, the scanning sequence is firstly high frequency in horizontal direction and low frequency in vertical (LHi) (i=3) , then low frequency in horizon and high frequency in vertical(HLi), and then high frequency in diagonal(HHi), others are (LHi-1), (HLi-1), (LH1), (HL1), (HH1)25-27. Figure 2. Parent-Child Dependencies of Subbands in SPHIT
Figure 2. The tree structure of the 3 level wavelet decomposition
SET PARTITIONING IN HIERARCHICAL TREES SPIHT is a fully embedded progressive wavelet coding algorithm that refines the most significant coefficients. The largest coefficients are transmitted first by using various tree searching routines. The SPIHT algorithm uses the partitioning of quad trees to keep insignificant coefficients together. In the implementation of SPIHT, the significant information is stored in three ordered lists as shown in figure 2.10-13.
• List of Significant Pixels (LSP) – contains coefficients that are significant or greater than the threshold. • List of Insignificant Pixels (LIP) – contains coefficients that are insignificant or less than the threshold. • List of Insignificant Sets (LIS) – contains sets of coefficients defined by tree structures which are insignificant or smaller than the threshold. The set excludes the coefficients corresponding to the tree or all subtree roots. The following represents the set of coordinates used. • O(i,j) – is the set of coordinates of the offspring’s of the wavelet coefficient at location (i,j). As each node can have four offspring’s (quad-tree), the size of O(i,j) is zero or four. • D(i,j) – is the set of all descendants of the coefficient at location (i,j). • L(i,j) – is the set of all coordinates of the descendants of the coefficient at location (i,j) except the immediate offspring’s of the coefficient at location (i,j). • H – is the set of all root nodes. The SPIHT algorithm consists of two main passes to code the image, a Sorting Pass and a Refinement Pass. The LIS and LIP entries are coded in the Sorting Pass and the LSP entries are coded in the Refinement Pass.
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The initialization of the threshold is the same procedure as that used in the EZW algorithm. The list of significant pixels (LSP) is set to empty or zero and the roots in the similarity trees of lists of insignificant pixels (LIP) and insignificant sets (LIS) are set to H and D respectively. The Sorting Pass begins by examining each coordinate in the LIP for significance. There are two comparison cases in the LIP. 1. If the coefficient is significant a ‘1’ is transmitted, followed by a bit for the sign of the coefficients to the LSP. The bit is ‘0’ for a positive sign and ‘1’ for a negative sign. 2. If the coefficient is not significant a ‘0’ is transmitted. After the LIP is examined the LIS sets are then examined. There are four comparison cases that make up the LIS component and they are as follows : 1. If the set at location (i,j) is not significant a ‘0’ is Transmitted 2. If the set at location (i,j) is significant a ‘1’ is transmitted. 3. If the set is confirmed significant and if it is a set of type D, the offspring coefficients are then individually checked. If the offspring coefficient is significant a ‘1’ is transmitted, followed by a bit representing the sign of the coefficient (‘1’ for a positive sign and ‘0’ for a negative sign). Next the coefficient is moved to the LSP. If the offspring coefficient is not significant a ‘0’ is transmitted. 4. If the set is confirmed significant and if it is a set of type L, each coordinate in O(i,j) is appended to the LIS as the root to a set of type D. These new entries in the LIS are examined during this pass. Thereafter the coordinate (i,j) is
removed from the LIS. Once each set in the LIS is processed a Refinement Pass then takes place. The Refinement Pass involves examining the coefficients of the LSP and transmitting the nth most significant bit of the coefficient at location (i,j). The remaining stages of the algorithm involve the same procedures described in the EZW algorithm. The SPIHT algorithm does not use scan coefficients like the EZW algorithm however, it is able to output and code descendants immediately. The SPIHT algorithm achieves higher compression performance than EZW due to its improved zerotree searching routine. This is because SPIHT does not scan coefficients in a predetermined order like the EZW which uses raster scanning, its scans through lists and encodes significant descendants immediately thus improving rate efficiency. RESULTS Original Image
Journal of Computer and Mathematical Sciences Vol. 1, Issue 7, 31 December, 2010 Pages (769-924)
Aziz Ur Rahaman et al., J. Comp. & Math. Sci. Vol. 1(7), 769-775 (2010) Scaled Image
773
Error after Compression In SPHIT
Error After Decompression in SPHIT
E rro r
12 34 56 78 111019 111324 111576 1289 2201 222324 222657 289
1.00E+00 1.00E-02 1.00E-04 1.00E-06 1.00E-08 1.00E-10 1.00E-12 1.00E-14
Harr DB4 Symlet Biortogonal
Medical Image
Level 4 scale Image Time taken for compression in SPHIT
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 Nural-Cell2
MRI-Head3
MRI-5
MRI-Knee
MRI-2
CT-Lung
Nural-Human
Retrieved Image of Harr, DB4, Symlet and Biorthogonal
CT-Hart
Harr DB4 Symlet Biortogonal CT-Brain1
Time
Time Taken For Compression In SPHIT
Medical Image
CONCLUSION Experiments has done on several medical images, we received good effects of Biorthogonal with SPHIT as compare with Haar, Daubecbies 4 and, Syamlet wavelet. REFERENCES 1. Antonini M, Barland M, Mathieu P, Daubechies I. Image coding using the Journal of Computer and Mathematical Sciences Vol. 1, Issue 7, 31 December, 2010 Pages (769-924)
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