Irreversible Compression of Medical Images

Bradley J. Erickson M.D.

The volume of data from medical imaging is growing COMPRESSION TECHNIQUES at exponential rates, matching or exceeding the de- cline in the costs of digital data storage. While methods to reversibly compress image data do exist, Most irreversible tech- current methods only achieve modest reductions in niques involve 3 steps: transformation, quanti- storage requirements. Irreversible compression can zation, and encoding. Transformation is a achieve substantially higher compression ratios lossless step in which the image is transformed without perceptible image degradation. These tech- from grayscale values in the spatial domain to niques are routinely applied in teleradiology, and of- ten in Picture Archiving and Communications coecients in some other domain. One familiar Systems. The practicing radiologist needs to under- transform is the Fourier transform used in re- stand how these compression techniques work and constructing magnetic resonance images MRI). the nature of the degradation that occurs in order to Other transforms such as the discrete cosine optimize their medical practice. This paper describes transform DCT) and discrete trans- the technology and artifacts commonly used in irre- versible compression of medical images. form DWT) are more commonly used for im- age compression. No loss of information occurs KEY WORDS: , , JPEG in the transformation step. Quantization is the step in which data integrity is lost. It attempts to minimize information loss by preferentially HE STORAGE and image transfer preserving the most important coecients, Trequirements of medical images have whereas less important coecients are roughly hampered attempts to implement picture ar- approximated, often as zero. Quantization may chiving and communications systems PACS) be as simple as converting ¯oating point values and teleradiology. Image compression recently to integer values. Finally, these quantized co- has been explored as a means of reducing costs ecients are encoded. This also is a lossless step of managing large image data sets. Lossless in which the quantized coecients are com- compression methods use redundancy within an pactly represented for ecient storage or image to more eciently transmit image infor- transmission of the image. mation while allowing perfect reconstruction, but these methods achieve only 2:1 to 4:1 re- duction for medical image.1 Irreversible or JPEG COMPRESSION ``lossy'' techniques can reduce images by arbi- trarily large ratios, but do not perfectly repro- The JPEG Joint Photographic Experts duce the original image. However, the Group) compression standard is a widely used reproduction may be good enough that there is no perceptible image degradation nor compro- From the Department of Radiology, Mayo Foundation, mised diagnostic value. This report reviews the Rochester, MN. application of image compression techniques to Correspondence to: B. J. Erickson, M.D., Department of medical imagery, focusing on the irreversible Radiology, Mayo Foundation, 200 First St. SW, Rochester, methods, including the JPEG2000 standard. MN 55905; tel: 507-284-8548; : 507-284-2405; e-mail: Following that is a review of measures for [email protected] Copyright Ó 2002 by SCAR 0Society for Computer Ap- evaluating compression algorithm performance plications in Radiology) and some of the recent results for wavelet Online publication 30 April 2002 compression. doi:10.1007/s10278-002-0001-z

Journal of Digital Imaging, Vol 15, No 1 March), 2002: pp 5-14 5 6 BRADLEY ERICKSON

Fig 1. The JPEG Algorithm. The image is ®rst separated into 8 ´ 8 pixel subimages. The DCT of each subimage then is computed. These coef®cients then are quantized using a quantization table 1for this illustration, each value is divided by 5). Finally, the quantized values are encoded from the upper left corner, with a `marker value' sent when there are no more nonzero values. compression method that includes both revers- BASIC WAVELET COMPRESSION ible and irreversible techniques, and has been described in detail by Wallace.2 Although JPEG Although the JPEG lossy algorithm is good was not designed for medical imagery ie, it was for many types of images, it has some draw- not de®ned for 12- or 16-bit intensity scales), it backs when applied to radiographic images. It has been adapted for radiologic images as de- degrades ungracefully at high compression ra- scribed by Gillespy and Rowberg.3 Figure 1 tios, with prominent artifacts at block bound- shows how the algorithm operates. It begins by aries, and it cannot take advantage of patterns dividing the image into 8 pixel ´ 8 pixel blocks. larger than the 8 ´ 8 pixel blocks. Wavelet- The DCT of each image block is computed, based compression schemes generally outper- resulting in an 8 ´ 8 block of spectral coe- form JPEG in terms of image quality at a given cients. Most of the information is concentrated compression ratio, and the improvement can be in relatively few coecients in the upper left dramatic at high compression ratios.4 corner of this DCT image. The DWT of an image is computed5 Fig 2) Quantization is performed next. In this using a pair of high- and low-pass ®lters with step, the coecients are approximated to values special mathematical properties. Many such that are easy to represent in a small amount of ``wavelet'' ®lters exist, but many groups have space. There is an 8 ´ 8 table called the quan- adopted the 9-tap/7-tap bi-orthogonal ®lters of tization table), which contains the values by Antonini et al,5 because they seem to work well which corresponding coecients are to be di- in real-world application.6 The 2 ®lters split the vided. By using di€erent values, spectral fre- image into 2 components or subbands in each quencies that are more important to the visual direction each is half the original size). This system can be preserved preferentially over less- produces 4 subband images, 1 containing the important frequencies. The resulting values low-frequency information, 1 each for the high- then are rounded o€ to the nearest integer. frequency information in the X or Y direction, JPEG encodes the quantized coecients by and 1 for high-frequency information in both X reordering them in a zigzag pattern. This places and Y. The process is repeated on the low- the largest values ®rst, with long strings of zeros frequency component, breaking it up into at the end, which can be eciently represented. ``high-low'' and ``low-low'' components. If this IRREVERSIBLE COMPRESSION 7

Fig 2. 2a. T1-weighted axial image of the head. 2b. Five-level DWT of this image. There is no difference in information between the two±only how it is represented. process is performed n times, an n-level discrete successful advanced wavelet techniquesÐit is created. A 5-level discrete yielded signi®cantly better results than conven- wavelet transform of an MRI is shown in Fig 2. tional wavelet compression with similar com- The DWT is e€ective for compression because it putational complexity.9 In addition to resulting e€ectively concentrates the information into a in ecient compression, it also transmitted the few coecients, with most other coecients be- compressed bitstream in which approximations ing zero or close enough to zero that they can be of the most important coecients regardless of considered zero without degrading the image. location) are transmitted ®rst. The values of Most wavelet compression algorithms these coecients are progressively re®ned, and compute a 4- or 5-level DWT, quantize the re- the most important remaining informa- sulting coecients, and eciently encode the tionÐthat which yields the largest distortion quantized coecients. The quantization is per- reductionsÐis transmitted next. It can be formed by dividing each coecient by a quanti- shown that such a transmission scheme with zation parameter and rounding o€ to the nearest uniform weighting) is the optimal way to de- integer. Having a larger quantization parameter crease the root-mean-square RMS) error in the will result in more coecients that are zero, and reconstructed image.9 hence, increases the compression ratio. Finally, encoding converts the coecients into values that can be stored or transmitted eciently. JPEG2000

Because JPEG was speci®ed for computers ADVANCED WAVELET TECHNIQUES that existed over a decade ago, and because new technologies like wavelet had surpassed JPEG It is the way that the nonzero coecients for many types of images, the JPEG group set are encoded that di€erentiates the advanced out to update the standard, which is now wavelet compression techniques. Figure 2 known as JPEG2000. For this paper, JPEG will graphically shows the hierarchical structure of refer to the older compression method, wavelet the DWT; advanced techniques capitalize on will refer to the family of speci®c wavelet this tree-based organization of the coecients. methods, and JPEG2000 will refer to the de- The most well known of these techniques is veloping standard. embedded zerotree coding, described by Shap- The JPEG2000 e€ort has been substantial. iro,7 and enhanced by Said and Pearlman.8,9 This group identi®ed a number of shortcomings The latter approach, termed set partitioning in of the JPEG standard that JPEG2000 would hierarchical trees SPIHT), was one of the early address. Among these were: 8 BRADLEY ERICKSON

1. Better performance at high compression medical images). Because it is still largely noise ratios that has been discarded,10 no structure can be 2. A single codestream that would support seen in the error image; these denoised images irreversible and generally are preferred by observers11 and ac- 3. Support for many types of images spe- tually may improve diagnostic accuracy.12 ci®cally including 16-bit medical images) These di€erences are most easily observed on a 4. Support for many di€erent environments computer display by rapidly switching between eg, high performance local area network the original and compressed image,13 or by or low-speed wide area network). subtracting the compressed image from the The algorithms included in JPEG2000 in- original image. clude the best wavelet methods and provides At moderate levels of compression, blurring for ¯exibility in the ®lters used and the wavelet can be seen as the quantization step more transform. It is radically di€erent in the way it roughly approximates coecients that describe encodes information to allow seamless transi- important features. At this point, recognizable tion from irreversible to lossless image trans- features will be seen in subtraction images. mission. It allows applications to apply At still higher levels of compression, blur- di€erent compression ratios to di€erent por- ring increases, and artifacts that are character- tions of an image. Finally, it provides mecha- istic for a particular algorithm appear. Two nisms for user-speci®able pixel accuracy. Not types of artifacts can be observed with the all of these features exist in the ®rst rollout of JPEG algorithm, the ``blocking'' e€ect and JPEG2000. The ®rst step only supports wave- ``line-pattern'' e€ect. Both result from decom- let image encoding. The more advanced fea- posing the image into nonoverlapping 8 ´ 8 tures will be ®nalized as later steps. The blocks and quantizing each block separately.14 interested reader is directed to the JPEG2000 Blocking artifacts do not occur on wavelet web page for detailsÐthe address is: http:// compressed images, because the transformation www..org/JPEG2000.htm. and quantization are calculated on the image as a whole rather than on small blocks, but a high degree of quantization of wavelet coecients EFFECTS OF IRREVERSIBLE COMPRESSION can generate wavelet or ``rice-shaped'' artifacts ON IMAGES with orientation and spatial extension that correspond with the subband of the most dis- The alteration in an image that has been torted coecients.14 Figure 4 shows examples irreversibly compressed depends heavily on of the types of artifacts that are characteristic of the characteristics of the image, the compres- the JPEG and wavelet algorithms at extreme sion algorithm, and the compression ratio compression levels. being used. When low compression rates are The great concern in using irreversible used, the quantization step largely discards compression for medical images is that subtle high-frequency noise in which spectral content ®ndings eg, a faint nodule on a chest ®lm) is represented by a large number of low would be ``lost'' in the compressed image, but magnitude coecients.10 At these very low this is not always the case. Subtle ®ndings may compression ratios, image degradation is im- be dicult for the human eye to discern because perceptible referred to as ``visually lossless''; of low contrast, but if they have a signi®cant Fig 3a). As noted above, JPEG2000 allows spatial extent, they are characterized by low users to specify the maximum change in pixel frequencies in the spectral domain, which are value permitted. Setting this value in the well preserved by wavelet compression and context of the viewing conditions can guar- most other compression schemes). Such subtle antee that the alteration always will be within ®ndings may remain visible even at high levels an acceptable range. of compression.14 As the compression ratio is increased, the Features that have their energy spread over ®rst perceptible changes typically are removal numerous smaller coecients in the wavelet or of ``salt-and-pepper'' noise obviously, this de- spectral domain are most vulnerable to com- pends on the image, but generally is true for pression for most irreversible compression IRREVERSIBLE COMPRESSION 9

Fig 3. In this ®gure, the top row of images shows chest width equal to 1% of the dynamic range of the image radiographs compressed 1using SPIHT wavelet method) at was used. Notice that at 10:1, the error image is noise. At 10:1, 50:1, and 200:1. A magni®ed subregion is shown in the 50:1 and 200:1, noticeable features can be seen in the error upper right corner. The absolute error image, using a display image. methods. An example of image content with sion tolerance'' is de®ned as the maximum energy distributed over numerous smaller co- compression in which the decompressed image is ecients is random noise, and, as noted earlier, acceptable for interpretation and aesthetics. this usually is discarded ®rst. Fine, irregular Digitized chest radiographs are very tolerant of textures also contain many small, high-fre- compression at least 40:1 for SPIHT wavelet11), quency coecients and tend to exhibit blurring digitized bone ®lms are moderately tolerant at moderate levels of compression. Examples between 20:1 and 40:1), and CT, MRI, and US include 1) white matter in a brain computed images exhibit fairly low tolerance to compres- tomography CT) image, 2) the trabecular sion less than 20:1). Unfortunately, one cannot pattern of bone radiographs, and 3) speckle in assign a single compression ratio for a modality an ultrasound US) image. These structural even for a given organ system. In a recent textures are good indicators of when compres- study15 applying JPEG compression to a large sion is introducing visible loss to the data. number of head CTs and head MRIs, there were It also is important to recognize that some images considered acceptable by 5 of 5 viewers types of images tolerate much higher levels of at ratios as high as 22, whereas other images compression than others, in which ``compres- were considered unacceptable at a ratio of 5.3. 10 BRADLEY ERICKSON

Fig 4. Examples of the types of artifacts that are charac- are wavelet-shaped artifacts that result from inaccuracies in teristic of the JPEG and wavelet algorithms at high com- coef®cients at this extreme compression ratio. 4c. Same pression levels. The left image, 4a, is the original CT subregion also at 40:1 with JPEG. Note the clear blocks in the subregion. 4b. Same subregion compressed at 40:1 using image. These are the 8 ´ 8 pixel subimages that are com- wavelet. Notice the ``rice-shape'' artifacts in the image. These pressed individually in the JPEG algorithm.

EVALUATION OF IRREVERSIBLE neuroradiologists 4,000 total ratings), none of COMPRESSION 47 measures correlated to any signi®cant degree with observer ratings. Although there is a gen- Because a single compression ratio cannot eral correlation, there is no consistent threshold be broadly applied to all modalities, or even to value that corresponds with the point at which all images of a single modality, the need for image degradation either becomes perceptible or careful evaluation of appropriate compression aesthetically unacceptable. Similarly, there is ratios becomes apparent. Three categories of little correlation between these measures and the methods have been used. 1) numerical analysis degradation of diagnostic quality as measured of pixel values before and after compression, 2) by diagnostic tasks. subjective observer evaluation focusing on aes- thetic acceptability and estimated diagnostic value, and 3) objective measurement of diag- SUBJECTIVE ASSESSMENT OF COMPRESSION nostic accuracy using blinded evaluation meth- ods. For both subjective and objective Many di€erent methods of using subjective evaluations, it is important to evaluate both observer perceptions of images exist to evaluate low- and high-frequency structures or patholo- the e€ect of compression. Many of the early gy. We will refer to this type of approach as a studies for example Ishiyaki et al21) used dual-frequency or dual-pathology method. rankings: if the observer correctly ordered the images from least compressed to most com- pressed, then de®nite di€erences are presumed NUMERICAL EFFECTS OF IRREVERSIBLE to exist at each step. However, it was dicult to COMPRESSION interpret cases in which rankings were out of order. Others used subjective ratings of the The most basic measure of compression ®- appearance of a pathologic process eg, liver delity is to compute the mean pixel error for the masses22 or multiple sclerosis lesions23). A compressed image. This is both familiar and weakness of this methodology is that one simple but fails to measure local degradations pathologic process may not have features sus- that can lead to loss of important information.16 ceptible to the compression method used, and Attempts to correlate numerical measures with the appearance of pathologic processes can be observer ratings or performance has borne little unpredictable, making it dicult for observers fruit.15,17±20 In the study by Erickson,15 200 CT to determine what is degradation and what is and 200 MR images of the head compressed at variation in appearance. Others have used two di€erent quality factors were rated by 5 ``image processing experts'' to de®ne a ``just IRREVERSIBLE COMPRESSION 11

Fig 5. Comparison of increases in disk density 1thick solid how improvements in disk density and network speeds have line), speed of wide area networks 1light solid line), the been matched by the radiology department's ability to create number of bytes of image data produced by CT 1dashed line), image data, and suggests that waiting for technology im- and MR scanners 1dotted line) in a working day. This shows provements to reduce costs will not be a successful strategy. noticeable di€erence'' for selecting the point at original JPEG in a large se- which compression resulted in a detectable dif- ries of CT and MR images of the head. That ference in a group of mammograms.24 study also found that JPEG and JPEG2000 One of the more popular and robust were not substantially di€erent in the maximum methods is to use a double-blinded 2-alternative ``acceptable'' compression ratio. forced-choice assessment.25±28 Using this tech- nique, one study had chest radiologists rate the appearance of several normal anatomic struc- DIAGNOSTIC EVALUATIONS tures seen on chest radiographs11 and found no di€erence in the subjective quality of any Most people agree that one can perceive structure up to a compression ratio of 40:1, and ``changes'' in the image long before an image only a slight preference for uncompressed im- is degraded enough to lose its diagnostic ages on 1 of the 11 structures vertebral body value,1,31,32 but this cannot yet be assumed for interspaces) at 80:1. Furthermore, a slight all compression methods, modalities, or diag- preference for compression at low ratios over nostic tasks. Because the role of the radiologist originals was noted. It is suspected that this is usually is to make a diagnosis, carefully de- because of the ®ltering properties of wavelet signed studies that measure the e€ects on clin- transformation eliminating noise.10 ical practice are essential. Many such studies Others have suggested an unblended 2-al- have evaluated the diagnostic accuracy of ternative choice, allowing the observers to rap- compressed images.12,28,31,33±35 Unfortunately, idly switch between images on a computer they are dicult to compare because di€erent screen. The observer then is asked to determine algorithms, image types, and evaluation para- whether there is a di€erence between the origi- digms were used. Although some types of nal and compressed image. This method re- compression may excel for certain features eg, cently was applied to a variety of medical maintaining low frequency contrast) they may images using several di€erent JPEG2000 meth- do less well with other features eg, high-fre- ods and the original JPEG algorithm.29 They quency edges). Therefore, it is the author's found that the proposed JPEG 2000 scheme opinion that receiver-operator characteristic appears to o€er similar or improved image ROC) studies evaluating both low- and high- quality performance relative to the current frequency features as well as textures are likely JPEG standard for compression of medical to be most valuable. Further, many studies use images, except for radiographs, in which the the original images as the gold standard, which performance for JPEG2000 was better. Sav- is biased against compression because any dif- cenko et al30 also compared JPEG2000 with the ference can only favor uncompressed images. 12 BRADLEY ERICKSON

An independent gold standard should be used There now is good evidence that irreversible whenever possible.25 compression can be used for medical image In general, JPEG does not achieve com- storage and transmission without compromising pression ratios as high as most wavelet meth- diagnostic value. However, it must be used in ods. The maximum ratio for JPEG is typically carefully managed, well-understood ways. An between 10:1 and 20:1 for most modali- important step toward achieving this is to have ties,23,24,36±38 perhaps because breaking the im- standardized methods for compression. ACR- age into small blocks decreases its ability to NEMA version 2.0 supports JPEG irreversible take advantage of low-frequency features larger compression, and there has been some e€ort to than 8 pixels. The logical improvement over extend Digital Imaging and Communications in JPEG is to stop breaking the image into small 1Medicine DICOM) to support wavelet com- blocks and perform the discrete cosine trans- pression. Working Group 4 Compression) of form over the entire image. For this ``full- the DICOM standards committee has repre- frame'' discrete cosine transform method, sentation on the JPEG2000 committee, and compression ratios of about 20:1 have been re- JPEG2000 has been approved as a DICOM ported to have no diagnostic degradation for standard, with ongoing work to adopt future chest radiographs33,34,39 with lower ratios for JPEG2000 features into DICOM. Wavelet mammography.40 It is important to note, methods appear superior to JPEG for medical however, that although no statistically signi®- images, but the lack of a single standard wavelet cant di€erence was detected, the trend was for method has hampered comparison of results JPEG to result in some image degradation at and cross validation. Adoption of JPEG2000 as these ratios, and it is possible that if enough a DICOM standard should hasten the applica- cases had been done, some di€erence would tion of wavelet compression in medicine. have been detected. Wavelet compression methods appear to perform better than JPEG, particularly for APPLICATION OF IRREVERSIBLE large-matrix images like radiographs.27,41 Using COMPRESSION TO MEDICAL PRACTICE the dual pathology approach, reports of com- pression ratios of as high as 80:1 showing equal The most common application of irrevers- or better performance than originals has been ible compression in radiology is teleradiology. reported.12 Imaging modalities such as MR, This application bene®ts tremendously because CT,22 and nuclear medicine require much lower of the low bandwidth connections most homes compression ratios, and the clear advantage of have. Although technologies like cable modems wavelet over JPEG is less clear. and-digital subscriber lines DSL) have in- creased bandwidth substantially, the need for compression seems to remain. We have found IRREVERSIBLE COMPRESSION AND DICOM that over the course of 25 years, the size in by- tes) of a `typical' CT examination as well as MR As more studies evaluating compression over the past 20 years) closely parallels the in- techniques and their e€ects on diagnostic and crease in speed of wide-area connections Fig 5). aesthetic appearance are performed, wider ac- In clinical practice, this means that the typical ceptance of irreversible compression will occur. emergency CT head for subarachnoid hemor- Adoption of a commercial standard will make rhage has become the nonenhanced CT followed supporting a irreversible compression method by the contrast-enhanced CT angiogram or an more appealing to vendors. Working Group 4 MRI with di€usion and perfusion images. of the DICOM standards committee image Another application of compression is to compression) has a liaison to the JPEG 2000 reduce the storage and bandwidth requirements committee for the purpose of maximizing the required to deliver images to clinicians.42 In this use-fulness of JPEG2000 for medical imagery, so system, all electronic images are transmitted to that there will be a well-recognized and sup- a server where they are compressed and stored. ported technology for compression of medical Because of the high compression ratio, several images. months of images are available immediately IRREVERSIBLE COMPRESSION 13 using a standard server. In addition, because images. Using irreversible compression in ev- images are decompressed at the desktop, the eryday practice can reduce signi®cantly the cost network bandwidth required to distribute these of delivering radiology services by reducing the images is reduced substantially. Finally, images information infrastructure required to deliver are stored in RAM and compressed, signi®- and store images. cantly reducing desktop computer resources demands. At the Mayo Clinic, this has reduced infrastructure costs by approximately $250,000 REFERENCES per year.43 In this application, image quality is 1. Karson TH, Chandra S, Morehead AJ, et al: JPEG satisfactory, and clinical acceptance has been compression of digital echocardiographic images: Impact on 44,45 overwhelmingly positive. image quality. J Am Soc Echocardiography 8:306-318, 1995 Medical-legal uncertainties are a signi®cant 2. Wallace GK: The JPEG still picture compression hurdle to widespread use of irreversible com- standard. Comm of the ACM 34:30-44, 1991 pression for diagnosis. It can be argued that 3. 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