Medical Image Compression Based on High Fidelity SPIHT

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(1)Medical Image Compression Based on High Fidelity SPIHT Shen-Chuan Tai. Yen-Yu Chen. Wen-Chien Yan. Institute of Electrical Engineering. Institute of Electrical Engineering. Institute of Electrical Engineering. National Cheng Kung University. National Cheng Kung University. National Cheng Kung University. [email protected]. [email protected]. [email protected]. Abstract. storage requirements. In medical applications, large. Due to the bandwidth and storage limitations,. volumes of digitized images are presented, so image. medical. before. compression is indispensable. In recent years, there. transmission. The set partitioning in hierarchical. are some standards built in American Industrial, like:. trees (SPIHT) algorithm is an efficient method for. ACR/NEMA[1], and DICOM[2], there are all. lossy and lossless coding of medical image. This. applied in lossy compression method. The SPIHT [3]. paper presents some modifications on the SPIHT. is the encoded algorithm for the medical images,. algorithm. It is based on the idea of insignificant. because of the SPIHT algorithm was an efficient. correlation of wavelet coefficient among the medium. method for lossy and lossless coding of still images.. image. must. be. compressed. In this. Section 2 reviews the original SPIHT algorithm. scheme, insignificant wavelet coefficients that. of Ref. [3]. Section 3 presents the modification and. correspond to the same spatial location in the. algorithm. medium subbands can be used to reduce the. comparison with JPEG2000 [4] and original SPIHT. redundancy by a combined function that modified. are presented in section 4 for several kinds of. SPIHT proposes. In the high frequency subbands, the. medical images. Section 5 presents the conclusion.. and high frequency subbands respectively.. in. detail.. Simulation. results. and. 2. Original SPIHT algorithm. modified SPIHT proposes dictator to reduce the interband redundancy. Experimental results show that. The SPIHT algorithm, introduced by A. Said. the proposed technique improves the quality of the. and W.A. Pearlman, adopts a hierarchical quadtree. reconstructed medical image in both PSNR and. [5][6] data structure on wavelet-based [7][8] image.. perceptual result when compare to JPEG2000 and. Figure 1 indicates the parent-child relationship. original SPIHT at the same bit rate.. through the subbands (quadtree). The original SPIHT. Keywords: SPIHT, JPEG2000. is briefly described as follows. The wavelet. 1. Introduction The. medical. images. include. coefficient are encoded and transmitted in multiple passes in the SPIHT algorithm.. computer. 1) Thresholding:. tomography (CT), magnetic resonance imaging (MRI), ultrasonography (US), and X-rays. The. In each pass, only the wavelet coefficients that. modalities provide flexible means for viewing. exceed threshold are encoded. The threshold T(u) is. anatomical cross sections and physiological states,. computed according to the expression T(u)=2P-u. and may reduce patient radiation doses and. (1). examination trauma. However, the medical images. ,where u=0, 1, 2, 3…, P denotes the pass number.. have large storage requirements. Because of the. And P= log 2. storage. capacity. limitation,. medical. image. compression techniques are needed to reducing the. max( c (i , j )) . (2). ,where c(i, j) is the coefficient at position (i, j) in the. 1.

(2) image.It just sends the max value to the decoder, and. LL3. the thresholds can be calculated by (1) and (2).. HL3. HL2. LH3. H H3. HL1. 2) Sorting pass: LH2. HH2. When u=n, n is integer. The pixel that satisfying T(n)≦|c(i, j)|＜2T(n) is identified as significant. c(i, j) is coefficient value. The pixel’s position and sign. LH1. HH1. bit must be encoded. 3) Refinement pass: The pixels that satisfying |c(i, j)| ≧2T(n) are. Figure 1: Parent-child relationship. refined by encoding the nth most significant bit. The original SPIHT algorithm ignores the. (those that had their coordinates transmitted in. correlation within the same level subbands. For the. previous sorting passing).. insignificant coefficients in the high frequency,. 4) Increment u by one, and go to step 2).. original SPIHT algorithm saves the space using. 3. Propose method. quadtree concept. In Figure 1, the nodes (coordinates. We propose a method to modify the original. in LL3) have no descendent trees; the nodes. SPIHT algorithm to be suitable for medical images.. (coordinates in LH3, HL3, and HH3) are the roots of. The original SPIHT algorithm was an efficient. the quadtree, and the remainder nodes (coordinates in. method for lossy and lossless coding of natural. other subbands) are tree nodes. There is large. images. We modify the original SPIHT algorithm,. correlation between LH3, HL3 and HH3. Table 1. according to the characteristic that the wavelet. shows the correlation of the same coordinates in LH3,. coefficients of medical images are more centered on. HL3, and HH3 in several kinds of medical images. the low frequency than those of natural images. And. (Figure. medical images have less edge than natural image. In. coefficients at equal coordinate in LH3, HL3, and. addition, the quality of medical compressed image. HH3 have at least an important value. Different. must reach an acceptable level in terms of the. condition means that the coefficients at equal. diagnosis.. coordinate in LH3, HL3, and HH3 have not. 2).. Same. condition. means. that. the. Table 1. Correlation in LH3, HL3, and HH3. important values. In xhead1 test image, percentage of. Same. Different. the insignificant coefficients at the same coordinate. condition. condition. in LH3, HL3, and HH3 is 97.5%. This statistics shows. Xhead1. 97.5%. 2.5%. that the percentage of the significant coefficients in. Angio2. 95.0%. 5.0%. subbands (not include LL3) is rare. These coefficients. Ctbone2. 93.4%. 6.6%. are essential to reconstruct image edges. Large. Ercp2. 95.6%. 4.4%. redundancies were hidden in presentation of these. Utheart3. 80.4%. 19.6%. coefficients. In utheart3 test image, percentage of the. Image. different condition slanted to higher than other test images. The main reason is that the utheart3 sample context is more complex than the others. Table 2 shows that the correlation of the same coordinate in. 2.

(3) LH1, HL1, HH1, LH2, HL2, and HH2 in all recursions. algorithm to decrease redundancy. After wavelet. in several kinds of images (Figure 2). Same condition. transform, the energy is centered on the wavelet. means that the treenode’s coefficients are at least. coefficients on low-low band. According to this. important on the quadtrees that’s roots are at equal. characteristic, the modified SPIHT algorithm divides. coordinate in LH3, HL3, and HH3. Different. wavelet-transformed image into three partitions. The. condition means that the treenode’s coefficients are. partitions include that α is a partition of the low. not important on the quadtrees that’s roots are at. frequency coefficients, β is a partition of the. equal coordinate in LH3, HL3, and HH3. That is, the. middle frequency coefficients, and γ. medical image that encoded by the original SPIHT. partition of the high frequency coefficients. C. algorithm has many redundancies.. represents that wavelet coefficients are significant or. is the. not, and (x, y) is the coordinate of the image. If the Table 2. Correlation in LH1, HL1, HH1, LH2, HL2, and HH2. wavelet coefficient c(x, y) is larger than threshold. Same. Different. condition. condition. Xhead1. 99.7%. 0.3%. set 0.. Angio2. 97.3%. 2.7%. α= {C(x, y) | (x, y) in LL3 }. (3). Ctbone2. 97.6%. 2.4%. β= {C(x, y) | (x, y) in LH3, HL3, HH3 }. (4). Ercp2. 97.4%. 2.6%. γ= {C(x, y) | (x, y) in LH2, HL2, HH2, LH1, HL1,. Utheart3. 80.3%. 19.7%. HH1}. Image. value T, then C(x, y) set 1. If the wavelet coefficient c(x, y) is smaller than threshold value T, then C(x, y). (5). As the follow, there are distinct concepts and ways of these partitions. A. For α= {C(x, y) | (x, y) in LL3} Each recursion in original SPIHT algorithm must send a bit map C(x, y) in LL3, descend the Angio2 (a). threshold value from T0 to T1( T1=T0/2), and decrease. Xhead1 (b). the reconstructive value from R0 to R1 ( R1=R0/2). Both threshold value T and reconstructive value R are geometric progression. To reduce the encoding bits, it is essential to decrease threshold value. Ctbone2 (c). Threshold value T1 was changed from T0/2 into T0/4. Ercp2 (d). in each recursion. It is also a geometric progression. Meanwhile, if the reconstructive value R is changed from T0/2 into T0/4, the exact value would be unbalance distribution. To avoid this phenomenon, the reconstructive value R should be calculated by. Utheart3 (e). R1=(T1+R0)/2, and the exact value would become. Figure 2: Test image.. balance distribution. The reduction of recursive. This work exploits the same level subband. number gains quite compression advantage, the bit. relation that is ignored by the original SPIHT 3.

(4) rate reduces 0.05~0.1 bpp (bit per pixel).. Q1={ LH2∪LH1 }. (7). B. For β= {C(x, y) | (x, y) in LH3, HL3, HH3}. Q2={ HL2∪HL1 }. (8). Q3={ HH2∪HH1}. (9). The modified SPIHT algorithm use a set w to reduce the redundancy in the partition β . The. We defined the set Su, u=1, 2, and 3. The set Su. original SPIHT algorithm does not think about. describes that the subtrree coefficients in Qt is. correlation in the same level subband. The modified. significant or insignificant. S1 is modified by. SPIHT algorithm adopts a set w, and w records what. following conditions in the set Q1.. subband between LH3, HL3 and HH3 has significant. S1(I, J)= 1, if LH1(x, y)=1, I=. coefficient. The modified SPIHT algorithm adopts a. x / 4 and J=  y / 4 . S (I, J)= 1, if LH (x, y)=1, I= x / 2 , and J=  y / 2 .. set w to eliminate the correlation in the same level. S1(I, J)= 0, otherwise.. 1. subbands.. 2. (10) (11). (12). There are the same steps in Q2 and Q3, and they. w ={ w (x, y) | LH3 (x, y)∪HL3 (x, y)∪HH3 (x, y)}. (6). result in S2 and S3. Because of the higher correlation. The partition w must be send to decoder. If w(x,. between three sets (S1, S2, S3), the modified SPIHT. y)=1, the bits of LH3(x, y), HL3(x, y),and HH3(x, y). algorithm creates a dictator that points out what. would be send to the decoder, not like the original. subband had significant coefficients. And the dictator. SPIHT send all the bit of LH3(x, y), HL3(x, y), and. d will decide what needs to send or not.. HH3 (x, y). If w(x, y)=0, nothing to be sent to decode.. d={d(m, n)| T1(m, n)∪T2(m, n)∪T3(m, n)}. The method can reduce about 0.1~ 0.2 bpp at the. Figure 3 shows the concept and framework of the. same PSNR (peak signal to noise ratio) value.. dictator. The oblique line block is the set Su, u=1, 2,. C. For γ= {C(x, y) | (x, y) in LH2, HL2, HH2, LH1,. and 3. This way even economized the bit to present. HL1, HH1}. the insignificant coefficients.. The. modified. SPIHT. algorithm. proposes. (13). dictator. dictator to reduce the redundancy in the partition γ. The significant coefficients in this partition are few, and the original SPIHT algorithm suggested that. LH2. HL2. HH2. using one bit to present whether the significant coefficient is in the quadtree or not. There is at least. LH1. HL1. HH1. one significant coefficient in the quadtree. And it presented as 1. If all of the nodes in the quadtree are. Figure 3. The dictator concepts and framework.. the insignificant coefficients, it presented as 0. There. According to the information of d, we can find. is quite large correlation in these subbands that. what subband has significant coefficients. And we. original SPIHT algorithm neglected, the modified. classify. SPIHT algorithm proposes dictator to solve this. coefficients into seven types. According to the. problem. According to the quadtree concept, we. significant coefficients in different subbands, we. know that there is a correction between LH1 and LH2,. encode differently.. these. subbands. that. have. significant. as the same reason in HL2, HL1, HH2, and HH1.. Seven types are as follow, (the LH means LH1. Therefore, we divide LH2, LH1, HL2, HL1, HH2, and. or LH2, HL means HL1 or HL2, HH means HH1 or. HH1 into three partitions Qt, t=1, 2, and 3.. HH2).. 4.

(5) Type 1: the significant coefficients are in LH.. electrocardiogram image at the bit rate of 1.4 bpp. Type 2: the significant coefficients are in HL.. with the PSNR value of 43.3 dB. Figure 4(b) shows a. Type 3: the significant coefficients are in HH.. decoded by JPEG 2000 electrocardiogram image at. Type 4: the significant coefficients are in LH and HL.. the bit rate of 1.4 bpp with the PSNR value of 40.6. Type 5: the significant coefficients are in LH and. dB. Figure 4(d) shows that the different image. HH.. between Figure 4(a) and Figure 4(c) has no intention.. Type 6: the significant coefficients are in HL and Table 3. Performance of proposed method.. HH.. PSNR of PSNR of. Type 7: the significant coefficients are in LH, HL and HH. For example, Type 6 is the significant. Bit rate. Original SPIHT. (bpp). (dB). PSNR of. Modified. JPEG2000 (dB). SPIHT (dB). coefficients in HL and HH. So we encode the bitmap. 0.35. 31.5. 34.5. 35.0. 0.80. 37.4. 37.9. 38.4. 1.40. 41.2. 40.6. 43.3. 2.77. 49.3. 48.00. 50.6. of LH and HH to show the significant coefficient position. And we encode the sign of significant coefficient.. 4. Simulation result. In Table 3, the PSNR values at different bit rate. Sonogram medical images are selected as test. are listed in comparison with original SPIHT, JPEG. data. It is gray-level image with a size of 512 x 512. 2000 and modified SPIHT. At the same bit rate, the. with 8 bits per pixels. We compare our propose. modified SPIHT PSNR values are absolutely higher. algorithm with JPEG 2000 that adopts original. than these of original SPIHT and JPEG 2000. The. SPIHT and TCQ (trellis coded quantization) [6]. The. test images (Figure 2) are several kinds of medical. performance is evaluated by PSNR (peak signal to. images include angiogram image, sonogram image. noise ratio) value. PSNR value is a mathematics. and X-ray image. Figure 5 illustrate the PSNR values. evaluation expression that can be calculated as. of our proposed method is better than the PSNR PSNR = 10log 10. 1 T. n −1 n −1. ∑ ∑ (x i =0 j =0. values of JPEG2000, and ref. [9] at the same bit rate. (14). 255 2. in several kinds of medical images.. − x 'i , j ). 2. i, j. 5. Conclusions In the paper, we introduce that original SPIHT. PSNR value has been accepted as a widely used quality. measurement. in. the. field. of. algorithm is proposed to achieve good performance,. image. and the modified SPIHT is modified from original. compression.. SPIHT according to the medical image characteristic.. The test images are showed in Figure 4. Figure. This is the first technique employed SPIHT to. 4(a) is a sonogram image with text. This property of. compress the medical images. The main goal of this. the image raises the difficulties of compression and. paper is to find a bit-rate reduced method that can. different with the other images. Even so, the decoded. save the store usage and achieve fast transmit of the. quality of texts and electrocardiogram (ECG). distance diagnosis in the future. Those modified. waveforms is still acceptable to diagnose, as show in. SPIHT reduce the redundancy more than original. Figure 4(c), a decoded by modified SPIHT. SPIHT and JPEG2000. And the modified SPIHT is 5.

(6) more suitable for compression of medical images. “JPEG2000 Image Compression Fundamentals,. than JPEG 2000.. Standard and Practice,” Kluwer Academic Publishers, 2002. Acknowledgement. [5] A. Munteanu, J. Cornelis, G. V. D. Auwera and. This research is supported partially by the National. P.cristea, “Wavelet Image Compression – The. Science Council of Taiwan under the contract. Quadtree. number of NSC 92-2213-E-006-081. Transactions on Technology in Biomedicine,. Coding. Approach,”. IEEE. vol.3, No.3, pp.176-185, September 1999. References. [6] Brian A. Banister and Thomas R. Fischer,. [1] American College of Radiology (ACR)/ National. “Quadtree Classification and TCQ Image. Electrical Manufacturers Association(NEMA). Coding,” IEEE Transactions and System for. standards Publication for Data Compression. Video Technology, vol.11, No.1, pp.3-8, January. Standards,. 2001. NEMA. Publication. PS-2,. [7] I. Daubechies, “Ten Lectures on Wavelets,”. Washington, DC, 1989. Capital City Press, Montpelier, Vermont, 1992. [2] Digital Imaging and Communication in Medicine. [8] S. Mallat, “A Theory for Multiresolution Signal. (DICOM), version 3, American College of Electrical. Decomposition: the Wavelet representation,”. Manufacturers Association (NEMA) standards. IEEE Transaction Patten Analysis and Machine. Draft, December 1992. Intelligence, vol.11, No.7, 674-693, July 1989. Radiology. (ACR)/. National. [9] Yung-Gi Wu and Shen-Chuan Tai, “Medical. [3] A. Said and W. A. Pearlman, “A New, Fast, and Efficient Image Codec Based on Set Partitioning. Image. Compression. in Hierarchical Trees,” IEEE Transactions. Transform Spectral Similarity Strategy,” IEEE. Circuits and System for Video Technology, vol.7,. Transactions on Information Technology in. No.3, pp.243-250, June 1996. Biomedicine, September 2001. [4] David S. Taubman and Michael W. Marcellin,. 6. vol.5,. by. Discrete. No.3,. Cosine. pp.236-243,.

(7) Figure 4 (a). Figure 4 (b). Figure 4 (c). Figure 4 (d). Figure 4: Sonogram test image (a) Original test image (b) Compressed by JPEG2000, bit rate=1.4 bpp, PSNR value=40.6 dB (c) Compressed by modified SPIHT, bit rate=1.4 bpp, PSNR value=43.3 dB. (d) Difference image between Figure 4(a) and Figure 4(c). 7.

(8) Medical image. PSNR value(dB). 50 45 40. Xhead1. JPEG2000. Angio2. Ref[9]. 35 Utheart3. Modified SPIHT. 30 0.22. 0.27 Bit rate(bpp). 0.55. Figure 5: Illustration the PSNR value in several kinds of medical images. 8.

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