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УДК 004.932.2:519.6
V.V. Moroz, O.O. Savkov
EFFECTIVE LOSSLESS AND NEAR-LOSSLESS COMPRESSION ALGORITHM FOR MEDICAL IMAGES
Introduction. The advanced medical imaging technologies, such as computerized tomography (CT), magnetic resonance imaging (MRI), ultrasonic and traditional radiology are fundamental tools for providing more efficient and effective healthcare systems and services. The digital representation of images is the motivation to spread of these technologies. Digital medical images have potential benefits in terms of achieving and probability. In addition they offer versatility, enabling or expanding its applications in medical imaging [1].
Image compression techniques take advantage of redundancy that occurs. There are different types of redundancy: spatial, temporal and spectral. Each compression methodology will exploit one of these redundancies. The research presented here will focus on the first of these three types of redundancies although the techniques can be used in the others also. It will make use of spatial redundancies since static spatial X-rays will be used. These are still the most dominant type of medical imaging data used today.
There are lossy and lossless techniques for image compression. Lossless techniques allow the perfect reconstruction of image after compression, i.e. decompressed back to the original state of the image without any loss of data. These methods are sometimes called reversible compression methods. Compression rates for lossless techniques vary typically in the range 2-3 times. Other lossy techniques do not allow the perfect reconstruction of the original image once it has been compressed. These methods are sometimes called irreversible compression methods. Compression rates for lossless techniques allow exceed 100 and more times. At high quality lossy levels (10-20 times), compression rates much greater than those obtained by lossless methods can be obtained while achieving visually indistinguishable results. That is, the human eye cannot detect a difference between the original image and the compressed-then-decompressed image with the lossy compression method. This technique called as near-lossless compression. However, the medical community has been very reluctant to adopt lossy algorithms in clinical practice. There is insufficient clinical research on the use of lossy compression applied to medical images. The new compression approach, which will be proposed here utilising a hybrid lossless/near-lossless method, can be made all lossless or all near-lossless.
The transformation coding is one of the most effective techniques among the existing compression algorithms. There are two more known transformation as DCT (Discrete Cosine Transform) and DWT (Discrete Wavelet Transform) which have been widely using in various applications for medical image manipulation for reducing the size of medical images. The most popular compression algorithms in use today in the medical community are lossless JPEG (Joint Photographic Experts Group) [2] and lossless Wavelet. JPEG has been adopted by the Digital Imaging and Communications in Medicine (DICOM) group in their widely adopted DICOM image file format, but the wavelet compression algorithm is gaining ground [3], [4], [5]. In fact, the DICOM Working Group added support for the JPEG 2000 standard into the DICOM format in November of 2001. It has also been adopted by ISO as a standard. JPEG 2000 is based on DWT.
After the transformation, the image data in spatial domain will be transformed into spectral domain to attain higher compression ratio. Based on the quantization strategy, coefficients of low frequency fields in the transformed domain are discarded and significant
coefficients are preserved to increase the compression ratio without inducing salient distortion. Further employment of coding technique yields lesser number of bits per pixel.
Considerable research efforts have been made for their efficient compression to facilitate storage and transmission. Indicative examples include wavelet-based applications for medical images compression [6], [7].The existent universal standard image compression algorithms not always result to effective compression for medical images. Therefore are developing a new compression algorithm [8], [9].
The subject of this investigation is the compression algorithm for gray-scale medical image using DICOM standard. The paper objective is a design and development of more effective compression algorithm for such image in comparison with existent.
Redundancy of medical images. Image compression and coding techniques explore three types of redundancies: coding redundancy, interpixel (spatial) redundancy, and psychovisual redundancy. The way each of them is explored is briefly described below.
Coding redundancy consists in using variable-length code words selected as to match the statistics of the original source, in this case, the image itself or a processed version of its pixel values. This type of coding is always reversible and usually implemented using look-up tables (LUTs). Examples of image coding schemes that explore coding redundancy are the Huffman codes and the arithmetic coding technique.
Interpixel redundancy is type of redundancy (sometimes called spatial redundancy, interframe redundancy, or geometric redundancy) exploits the fact that an image very often contains strongly correlated pixels. In other words, there are large regions whose pixel values are the same or almost the same. This redundancy can be explored in several ways, one of which is by predicting a pixel value based on the values of its neighboring pixels. In order to do so, the original 2-D array of pixels is usually mapped into a different format, e.g., an array of differences between adjacent pixels. If the original image pixels can be reconstructed from the transformed data set the mapping is said to be reversible. Examples of compression techniques that explore the interpixel redundancy include: Constant Area Coding (CAC), (1-D or 2-D) Run-Length Encoding (RLE) techniques, and many predictive coding algorithms such as Differential Pulse Code Modulation (DPCM).
Concerning the psychovisual redundancy, many experiments on the psychophysical aspects of human vision have proven that the human eye does not respond with equal sensitivity to all incoming visual information; some pieces of information are more important than others. The knowledge of which particular types of information are more or less relevant to the final human user have led to image and video compression techniques that aim at eliminating or reducing any amount of data that is psychovisually redundant. The end result of applying these techniques is a compressed image file, whose size and quality are smaller than the original information, but whose resulting quality is still acceptable for the application at hand. The loss of quality that ensues as a byproduct of such techniques is frequently called quantization, as to indicate that a wider range of input values is normally mapped into a narrower range of output values thorough an irreversible process. In order to establish the nature and extent of information loss, different fidelity criteria (some objective such as root mean square (RMS) error, some subjective, such as pairwise comparison of two images encoded with different quality settings) can be used. Most of the image coding algorithms in use today exploit this type of redundancy, such as DCT-based (Discrete Cosine Transform) algorithm at the heart of the JPEG encoding standard. And so JPEG is most used in DICOM files for medical image compression.
However these images have high level of entropy and so they are very hard to compression. For example, DICOM MRI image is grayscale image with 12 or 16 bit per pixel and its side length mainly equal a power of two. Another important distinctive feature of MR images is that not always whole image contains significant information. MR scanners capture
image as circular area. The negative of MRI image is presented on Fig. 1.
Fig. 1. Typified MRI and ultrasonic images.
This specific feature can be used for compression of MRI images with more efficiency.
X-Ray image has the same feature, but it's region of interest may vary from circular. The negatives of X-Ray images are presented on Fig. 2.
Fig. 2. Typified X-Ray images.
This feature allows more effective image compression, using non-significant information.
Quad-tree based compression algorithm. This algorithm was created for lossless compression of grayscale 16-bit depth MR DICOM images, but it could be used for radiology, ultra-sonic and other types of the medical images. It also may be easy modified for near lossless compression.
Let / is a grayscale 16-bit depth image with 2jV linear dimensions. Quad-tree decomposition for this image is presented on Fig. 3.
If / has the same brightness level then it may be encoded as coordinates (^y) of upper left corner, a length of quads side and current level of brightness. If / have different levels of brightness I is divided into four squares with 2jV~1 linear dimension.
In case of near-lossless compression I is divided into four squares when a brightness level differs on more than I levels, where I is given integer value. This value is depended on
psychovisual system of human and it influences on a quality of reconstructed image. In this situation rounded to integer average brightness level of square is stored. It is a kind of two-dimensional quantization. This process repeats until whole image is divided by squares or until the linear dimensions of squares will be less than 2". The result of this step is quad-tree with size of quads more than 2".
Fig. 3. Quad-tree decomposition of MRI of the brain.
Thus we will have the array of vectors P and each vector has elements (Coordl, Coord2, S, Value\ where:
CooreEl Coordl - coordinates of the left top corner;
S - power of two for size of square;
Value - brightness value;
for all squares with size more 2", n > 0.
The array of vectors is compressed by Arithmetic coding. The arrays of unprocessed pixels U are compressed by Huffman coding as it is more effective for large capacity of data. A decoding process is presented on the Fig. 4.
Huffman decoding
Arithmetic decoding
Quad-tree reconstruction
•e
Fig. 4. Decoding process of compressed image.
The current quad-tree is using for construction of logical mask for processed pixels. It is needs for further construction of array of unprocessed pixels. For near-lossless compression mode, a brightness array is quantized. These pixels form array that is compressing by arithmetic encoder.
If size of image I differs from 2jV, an image is supplemented to 2jV by adding zero rows and columns. Computational complexity of this algorithm is asymmetric, because quadtree decomposition is created only for compression.
Experimental results. The proposed algorithm BTCA was tested on large quantity of test MRI images and compared with other lossless compression algorithms as JPEG, 7z (LZMA Ultra). The size of DICOM's files is 515 KB for all images. Besides mentioned algorithms also JPEG2000-Lossless was tested (it is not presented here). As expected, the
algorithms what based on decorrelation transform do not good result. The explanation of this is in the structure of such images. Results are presented in Table 1. (an image size is in KB).
CR (compression ratio) varies within 3.79-7.25 but the proposed algorithm gives a better result for all test images. A fee for high CR is a growth of computational complexity. Nevertheless the time encoding is not critical value for DICOM storage system. An exception is for communication system.
Table 1: Lossless Algorithm Comparison.
Image JPEG LZMA Ultra BTCA CR
0001 97 83 71 7.25
0002 110 99 83 6.20
0003 122 113 96 5.36
0004 132 123 105 4.90
0005 138 129 111 4.64
0006 142 134 115 4.48
0007 144 139 118 4.36
0008 146 140 120 4.29
0009 150 144 124 4.15
0010 155 148 127 4.06
0011 156 151 130 3.96
0012 157 151 131 3.93
0013 158 154 132 3.90
0014 160 156 134 3.84
0015 161 156 136 3.79
0016 159 154 133 3.87
0017 158 152 130 3.96
0018 158 152 130 3.96
0019 157 150 129 3.99
0020 55 147 127 4.06
0021 154 146 126 4.09
0022 152 145 125 4.12
Conclusion. In the paper new compression algorithm was presented. There are several popular approaches for encoding as Huffman encoding, Lempel-Ziv encoding, arithmetic encoding and run-length encoding, but better result is possible only on the assumption of maximal extraction of inter-pixel correlation. It showed that Lempel-Ziv encoding methods achieve higher compression than compression ratios resulting from using Huffman encoding. However quad-tree decomposition with Huffman encoding for large array and arithmetic encoding for short one is more effective. The received results confirm that.
The near-lossless compression eliminates the redundant and high frequency data from an image, which is usually outside the range of human visual perception. This results in much higher compression ratios, typically more 10 or greater, but with some irretrievable data loss.
REFERENCES:
1. Rafael C. Digital Image Processing/ C. Rafael Gonzalez and E. Richard //Pearson Education. - Delhi, 2002.
2. Wallace G.K. The JPEG still picture compression standard/ G.K. Wallace// Communications of the ACM. -1991.-Vol. 34, No. 4. - P.30-44.
3. Zukoski M.J. A novel approach to medical image compression / M.J. Zukoski, T. Boult and T. Iyriboz// Int. J. Bioinformatics Research and Applications. - 2006.-V. 2, No. 1. - P. 89-103.
4. Iyriboz T.A. A comparison of wavelet and joint photographic experts group lossy compression methods applied to medical images / T.A. Iyriboz , M.J. Zukoski., K.D. Hopper and P. L. Stagg // Journal of Digital Imaging, May. - 1999.-12.- P.14-17.
5. Said A. A new, fast and efficient image codec based on set partitioning in hierarchical trees/ A Said and W.A. Pearlman // IEEE Transaction on Circuits system for video Technology. - 1996.- 6.- P. 243-250.
6. Kai X. HVS-based medical image compression / X. Kai, Y. Jie, Z. Y. Min, and L. X. Liang // European Journal Radiology. - 2005.- 55, No.1.- P. 139-145.
7. Wang J.Z. Wavelets and imaging informatics: A review of the literature/ J.Z. Wang // J. Biomed. Inf. -2001. - Vol. 34, No. 2. - P. 129-141.
8. Wu X. L™ Constrained High-Fidelity Image Compression via Adaptive Context Modelling/ X. Wu and P. Bao // IEEE Transactions on Image Processing.--2000.- 9, No. 4. - P.536-542.
9. Weinberger M. The LOCO-I Lossless Image Compression Algorithm: Principles and Standardization into JPEG-LS/ M. Weinberger, G. Seroussi and G. Sapiro // IEEE Transactions on Image Processing.-2000.- 9, No.8, P.1309-1324.
Moroz V. V. is with the Computational Mathematics Department, Odessa National University.
Scientific interests:
- image and video processing, mathematical modeling.
Savkov O. O. is an undergraduate of the Institute of Mathematics, Economy and Mechanics, Odessa National University. Scientific interests:
- image processing and data compression, wavelet analysis.
