Wavelet Compression and Segmentation of DigitalMammograms

Bradley J. Lucier, Maria Kallergi, Wei Oian, Ronald A. DeVore, Robert A. Clark, Edward B. 5aff,and Laurence P. Clarke

An initial evaluation of Haar wavelets is presented inthis study for the compression of mammographicimages. Fifteen mammograms with 105 11m / pixel reso-lution and varying dynamic range (10 and 12 bits perpixel) containing clustered micro calcifications werecompressed with two different rates. The quality andcontent of the compressed reconstructed images wasevaluated by an expert mammographer. The visualiza-tion of the cluster was on the average good butdegraded with increasing compression because of thediscontinuities introduced by these types of waveletsas the compression rate increases. However, the arti-facts in the decoded images were seen as totallyartificial and were not misinterpreted by the radiolo-gist as calcifications. The classification of the parenchy-mal densities did not change significantly but themorphology of the calcifications was increasingly dis-torted as the compression rate increased leading tolower estimates of the suspiciousness of the clusterand higher uncertainties in the diagnosis. The uncom-pressed and two sets of compressed images were alsoprocessed by a wavelet method to extract the calcifica-tions. Despite the fact that the segmentation algo-rithm generated several false-positive signals in highlycompressed images, all true clusters were successfullysegmented indicating that the compression processpreserved the features of interest. Our preliminaryresults indicated that wavelets could be used to achievehigh compression rates of mammographic imageswithout losing small details such as microcalcificationclusters as well as detect the calcifications from eitherthe uncompressed or compressed reconstructed data.Further research and application of multiresolutionanalysis to digital mammography is continuing.Copyright @ 1994 by W.B. Saunders Company

display. Data compression methods could facili-tate these processes but they should also satisfythe requirements for highly accurate reconstruc-tion of mammograms.

Severallossless and lossy compression meth-ods have been investigated for medical imagingapplications.4,5 Lossless compression methodsapplied to mammography include tree-basedcodes which represent a large class of variable-length encoding schemes and arithmetic codes.6Lossless methods have the advantage that theycan be applied anywhere because such com-pressed images are reconstructed without error.Their disadvantage is the small compressionrates, on the order of 3:1. In contrast, lossytechniques can achieve very high compressionratios at the expense of errors in the recon-structed images. A new class of lossy compres-sion algorithms is currently under developmentthat could offer data with no visible artifacts}.8Receiver operating characteristic (ROC) analy-sis on lossy compression showed that it ispossible to use lossy techniques in medicalimaging, provided that the diagnostic power isnot lost or diminished.9,lo Such methods arereferred to as "visually lossless" and hold prom-ise for effective mammogram compression. Theproperties of the human visual system are suchthat some losses can be tolerated without affect-ing the visual evaluation of an image which,despite the losses, appears identical to theoriginal. Furthermore, even visually lossy im-

KEY WORDS: wavelets, image compression, segmen-tation, digital mammography.

D IGITAL MAMMOGRAPHY involves ei-ther the digitization of screen-film mam-

mograms or the direct digital acquisition ofx-rays. In both cases, the requirements for highresolution images with high dynamic range leadto large data sets, on the average about 50Mpixels with dynamic ranges of 12 bits perpixel.l'z In addition, screening digital mammog-raphy implies real time availability to the radi-ologist of a series of such images per patient forcomparative study and accurate diagnosis.3 Suchlarge image database challenges the existingtechnology for data storage, transmission, and

From the Department of Mathematics, Purdue University,W Lafayette, IN, Departments of Radiology and Mathematics,University of South Florida, Tampa, FL, and the Departmentof Mathematics and Statistics, University of South Carolina,Columbia, SC.

Supported in part by the Office of Naval Research (ContractsNOOO14-91-J-1152 and NOOO14-91-J-1076), the Anny HighPeifonnance Computing Research Center at the Universi/}' ofMinnesota, and the H. Lee Moffitt Cancer Center & ResearchInstitute at the University of South Florida.

Address reprint requests to Laurence P. Clarke, PhD,Department of Radiology, University of South Florida, 12901Bruce B. Downs Blvd, Box 17; Tampa, FL 33612-4799.

Copyright:O 1994 by WB. Saunders Company0897-1889/94/0701-0005$03.00/0

Journal of Digital Imaging, Vol 7, No 1 (February), 1994: pp 27-38 27

LUCIER ET AL28

had a dynamic range of 10 bits per pixel (1,024gray levels) and eight had a dynamic range of 12bits per pixel (4,096 gray levels). The opticaldensity range selected for the digitization wasdifferent for each mammogram and it wasdetermined from the optical density of thebrightest spot on the films. This allowed themaximization of the intensity differences be-tween the various breast features and thusmaximum separation in pixel values betweenthe microcalcifications and the surrounding tis-sues. Sections of the images (512 x 512 pixels)containing the calcification cluster were usedfor compression and segmentation. The sizes ofthe original images were 327,680 and 393,216bytes for the 10-bit and 12-bit files, respectively.

Image CompressionA mathematicaf theory that analyzes the

efficiency of wavelet-based image compressionschemes is described in detail elsewhere. I I The

method used in this study for the compressionof mammographic images is identical to thatused to report the results of Fig 14 in DeVorel1and only a brief description of the method willbe presented here.

A wavelet-based compression algorithm isconstituted of three steps:11 (1) A wavelet familyis selected that will be used to decompose theimage. Each wavelet family has different smooth-ness characteristics and approximation proper-ties; in this article, the Haar wavelets are chosenbased on our previous experience. II (2) A quan-tization strategy must be selected. Each strategyis equivalent to a metric with which the differ-ence between the original and reconstructedimages will be measured. Two popular choicesof metric are the L2 (mean-square error) and Ll(mean-absolute error) metrics. If the pixels ofthe original image fare denoted by Pj,j = (jl,j2)and 1 ~ jl,h ~ 51?, and the pixels of thereconstructed image f are denoted by Pi' thenthe mean-square error is defined by

ages may be acceptable, when artifacts due tolossy compression can be recognized as entirelyartificial and do not disturb the discriminatinganalysis followed by the radiologist to reach adiagnosis. Finally, it should be pointed out thatthe use of lossy compression methods dependson the application, the image, and the aims of a

particular project.5One of the most promising lossy compression

approaches uses wavelets.11 Wavelets have beenalready used for mammogram segmentation,12,13enhancement,12 and compression.' The presentstudy focuses on the use of Haar wavelets forthe compression of mammographic images con-taining clustered calcifications. Uncompressedand compressed reconstructed data were alsoprocessed with a segmentation algorithm thatused a wavelet transform. A radiologist expertin mammography evaluated the quality of thecompressed images and the usefulness of thesegmented data based on a questionnaire de-signed to provide a qualitative description of theoriginal and compressed images. An extensiveROC clinical evaluation is beyond the scope ofthis research that aims primarily at preclinicalevaluation and algorithm optimization. The pur-pose of the study is three-fold: (1) to applydifferent levels of compression to digital mam-mograms and determine the limits of acceptablelosses, which will serve as a first criterion to theselection of an optimum wavelet compressionapproach, (2) to evaluate the quality of the lossycompressed images and the effect of the lossesin the radiologist's diagnosis, and (3) to showthe feasibility of extracting the calcificationsfrom the uncompressed and compressed datawith a wavelet-based segmentation algorithm, aprocess that could provide an additional crite-rion to the design of an optimum compressionmethod for digital mammography.

MATERIALS AND METHODS

MammogramsFifteen screen-film mammograms were con-

sidered as a first test of the compression algo-rithm. They aft contained one biopsy-provenmalignant cluster of calcifications superim-posed on parenchymal tissues of varying den-sity. All mammograms were digitized at a reso-lution of 105 ~m/pixel with a DuPont NDTScan II digitizer (Delaware, VA). Seven images

1

Ilf-.1112: = (~::t: Ipj _pjI2)~

and the mean-absolute error is defined by

-I",\:,Ilf -fill: = N .£..Ilpj -Pj I,J

where N is the number of pixels in the image; in

WAVELETS IN DIGITAL MAMMOGRAPHY 29

with a mean-square error of 64 in a 12-bit image(or of 4 in an 8-bit image). Based on this reason-ing, 15 mammograms were compressed twicewith the parameters summarized in Table 1.

The compression algorithm was implementedin FORTRAN and C-Ianguage and run on aSun Microsystems (Mountain View, CA)SPARCstation 2. The time of compression was10 se~onds per image.

Image SegmentationA wavelet-based segmentation method has

been previously applied to uncompressed digi-tal mammograms for the extraction of calcifica-tion clusters.12 Those results were very promis-ing with 100% sensitivity and only .1 false-positive clusters per image. The performance ofthis algorithm on the current uncompressed andcompressed data could, therefore, be a firstindication of the effect of wavelet compressionon the design of computer assisted diagnosismethods or compensate for the losses allowinghigher compression rates. Based on this hypoth-esis, the images of this study were processed asfollows: (1) They were enhanced with a tree-structured nonlinear filter. As mentioned indetail elsewhere, this filter consists of a series ofcentral weighted median filters which are ap-plied to the image in three steps. This processallows effective suppression of the image noisewithout removing image detail.12.14 (2) The en-hanced image was decomposed using a two-channel wavelet transform into four indepen-dent subimages which contain different types offrequencies.12.15.16 The first subimage containsthe low frequencies of the image, the secondcontains the vertical high and horizontal lowfrequencies, the third contains the vertical lowand horiZontal high frequencies, and the fourthcontains the high frequencies in both directions.(3) A wavelet reconstruction process was per-formed using the last three sub images resultingin one image that contains features correspond-

this study N = 512 x 512 = 262,144. Thequantization strategy determines the relativeimportance of contrast and spatial frequency inchoosing which features of the image can beremoved while causing minimal visual degrada-tion. It was previously reported!! that for 512 x512 natural images viewed at a standard viewingdistance of four times the width of the image,the contrast-frequency tradeoff implied by theLl error metric more closely matched the char-acteristics of the human visual system than thecontrast-frequency tradeoff implied by the choiceof the L2 error metric. Mammograms are notviewed by radiologists solely at arm's length,however, and it was observed with earlier 8-bitdigitized mammograms that the L2 metric bal-anced the degradation of the edges and shapesof microcalcification clusters with the degrada-tion of the structure of architectural distortionsin the underlying tissues. The Ll quantizationstrategy at a given level of compression tendedto preserve the structure of architectural distor-tions better than the L2 strategy, at the expenseof smoothing away evidence of microcalcifica-tions. Therefore, for our first controlled study,we chose to use only the L2 quantization strat-egy. The results of this work will serve asguidelines for our future investigations of other

quantization strategies.(3) After choosing the wavelets and quantiza-

tion strategy, one must select a parameter calledthe maximum quantization interval, q, whichroughly determines the local error. The greaterthe q is, the greater the compression, but alsothe greater the error. When dealing with imageswith different dynamic ranges (in this study, forexample, seven of the images have 1,024 greylevels and eight have 4,096 grey levels), it isuseful to consider the normalization of theintensity range to a minimum of 0 and a maxi-mum of 1. This can be done by dividing all pixelvalues by the maximum grey scale value 2K,where K = 10 or 12 in this study. Then, theparameter that best estimates the local visualquality of the image is q/2K. Thus, q = 512 forour 12-bit images leads to comparable compres-sion ratios and local image quality as q = 128 forour 10-bit images. When comparing mean-square errors, it is again useful to divide by themaximum grey scale. Thus, a mean-square errorof 16 in a 10-bit image is roughly comparable

Table 1. Parameters Used for Two Compression Runs of 15

Mammograms

128-10-bit images512-12-bit images

p=2

256-10-bit images

1024-12-bitimages

p=2Space Lp

q. maximum quantization interval.

30 LUCIER ET AL

ing to calcifications. Details of this algorithmare described elsewhereI2,15,16 but it should bementioned that the proposed wavelet segmenta-tion could be further improved and optimizedfor compressed images.

Once the parameters of the segmentationalgorithm are optimized for the uncompressedmammograms, they are kept constant for bothuncompressed and compressed images. Thesoftware was written in C-language and run on aSun Microsystems (Mountain View, CA)SP ARCstation 2. The time of segmentation wasabout 5 minutes per image.

description of the visual characteristics of thequality of the digitized and compressed recon-structed images, to determine the degree ofassistance of the segmentation algorithm to therecognition of the calcification clusters, and tohave a first estimate of the acceptable limits forthe lossy compression of mammograms.

Digital images were displayed on a 19" colorSun monitor with 1,152 x 900 pixels usingSunVision 1.2 software; no processing of thedisplayed images was permitted. It should benoted that current technology limits the displayto 8 bits per pixel or 256 grey levels. WithSunVision 1.2, the lowest values in the 10-bit or12-bit images are scaled to 0, the highest valuesto 255, and the intervening values are scaledproportionately between 0 and 255; lower andhigher values are clamped to 0 and 255, respec-tively.

Evaluation Protocol

A questionnaire was fomled for the qualita-tive visual analysis of the original, compressed,reconstructed, and segmented versions of the 15cases. It included nine questions shown in Table2. Each question was rated on a scale of 1 to 5.There were 7 images to be evaluated per case,namely the film, the digitized image, the recon-structed image from the first compression, thereconstructed image from the second compres-sion, and three segmentation results. A radiolo-gist expert in mammography was asked to readall 105 images and complete one questionnairefor each one although some of the questionswere not applicable to all of them. The objectiveof this evaluation was to obtain a standard

RESULTS AND DISCUSSION

Figures 1 and 2 present sections of digitizedmammograms (105 !.Lm, 12 bits per pixel) beforeand after compression. The mammograms con-tain one cluster of biopsy-proven, malignantcalcifications, the location of which is deter-mined by an expert mammographer and isindicated by an arrow. There is a variation inthe subtlety of the calcifications caused mainlyby the density of the surrounding or superim-

Table 2. Questionnaire Used for Qualitative Evaluation of Compressed Images and Segmentation Data

1. Visualization of calcification cluster 1Poor1-51

Low1

Definitely

Norma!

1Extreme

1Extreme

1Extreme

2 4 5Excellent

>305

High5

DefinitelyCancer

5None

5None

5None

2. Number of calcifications3. Parenchymal density classification

6.102

11-203

21-304

2 44. Degree of suspicion 3Undefined

5. Distortion of calcifications' morphology 2 3 4

6. Distortion of parenchyma 2 3 4

3 47. Degree of losses (overall) 2

8. Degree of confusion secondary to false

positive artifacts 5None

5None

1Extreme

1Extreme

2 3

2 3 49. Degree of assistance of segmentation

process--

One answer sheet was used for each image, namely the original film, the digitized mammogram, the compression number 1, and the

compression number 2, although some of the questions were not applicable to all images.

WAVELETS IN DIGITAL MAMMOGRAPHY 31

Fig 2. (A) Section of digitized mammogram (1051J.m, 12 bitsper pixel) with a more subtle calcification cluster indicated byarrow. (8) Wavelet compressed and reconstructed image withmaximum quantization interval q = 512; mean-square error,54.61; and compression ratio 22:1. (C) Wavelet compressedand reconstructed image with q = 1,024; mean-square error,74.51; and compression ratio 55:1.

Fig 1. (A) Section of digitized mammogram (105IJ.m, 12 bitsper pixel) with a calcification cluster of average subtletyindicated by arrow. (B) Wavelet compressed and recon-structed image with maximum quantization interval q = 512;mean-square error, 37.14; and compression ratio 53:1. (C)Wavelet compressed and reconstructed image with q = 1,024;mean-square error, 48.99; and compression ratio 123:1.

32 LUCIER ET AL

posed parenchymal tissues. The mammogramof Fig lA has a parenchymal density of about50% and the mammogram of Fig 2A has adensity of about 75% of the total breast area.The compressed reconstructed images with amaximum quantization interval of 512 are shownin Figs IB and 2B. Figures lC and 2C show thecorresponding compressed reconstructed im-ages using a maximum quantization interval of1,024. Because of the differences in the paren-chymal density and the noise content, differentcompression ratios and different mean-squareerrors were obtained for the same q value.

The results of the compression can be seenbetter in Figs 3 and 4 where horizontal cross-sections through the calcification cluster of theimages in Figs 1 and 2, respectively, are plotted.The continuity and smoothness of the pixels inthe original images is increasingly lost as themaximum quantization interval and thus thecompression rate increases. The higher compres-sion ratio observed for the first mammogram isdue to its lower parenchymal density which alsoaccounts for the fact that the calcifications arebetter preserved in this case even at the higher

compression (q = 1,024). On the other hand,the data are smoother in the second mammo-gram where smaller compression rates are ob-tained. In general, the compression effects aredifferent for mammograms of low and highparenchymal densities. Furthermore, mammo-grams digitized at higher dynamic range (moregray scales) allow higher compressions with lessinformation loss.

Table 3 lists the mean-square errors and thecompression ratios achieved in the two compres-sion sets. The compression ratios were deter-mined by the number of bytes of the originalfiles divided by the corresponding compressedsizes. It is best to interpret the mean-squareerrors by dividing by the number of gray scalesin each image. Therefore, for the first compres-sion results of Fig 1B, the mean-square error is37.14/4,096 or 9% whereas for the secondcompression of Fig 1 C, it is 48.99/4,096 or 1.2%.Similarly, the mean-square errors of the imagesin Figs 2B and 2C are 54.6/4,096 or 1..3% and74.51/4,096 or 1.8%, respectively.

Figures 5 and 6 show the segmentation resultsfor the images in Figs 1 and 2. The algorithm

B

20001

IIf-DO!

1000

500 U"-.,.J"I."",~0 100 200 300 400 500

Fig 3. Horizontal cross-sec-tions through the calcificationcluster shown in Fig 1, A throughC. (A) Original uncompresseddata. (B) compressed data withq = 512, and (C) compresseddata with q = 1,024.

WAVELETS IN DIGITAL MAMMOGRAPHY33

0 100 200 JOO 400 500

0 100 200 300 400 500

Fig 4. Horizontal cross-sec-tions through the calcificationcluster shown in Fig 3, A throughC. (A) Original uncompresseddata, (8) compressed data withq = 512, and (C) compresseddata with q = 1,024.

5 0 0 0

t -.,.J\J'~~--'~~""""""'-..,.J/~"-'~~= 4lJDO C

3000

2000

1000:

0 100 200 300 400 500

was successful in segmenting the calcificationsfrom the uncompressed images. The loss ofcontinuity and smoothness of the pixel in thecompressed data affects the results of the seg-mentation algorithm in that it generates false-positive spots which, although not of the sameintensity as those corresponding to the calcifica-

tions, are considered as distracting by the radi-ologist, particularly for the higher compression(set number 2). This indicates that either adifferent segmentation algorithm should be de-veloped for compressed data or a differentcompression method should be used to avoidabrupt discontinuities in the compressed im-

Table 3. Dynamic Ranges. Mean-Square Errors Measured in Gray Scales and Compression Ratios for the Two Compression SetsThat Have Different Maximum Quantization Intervals

36.0237.1448.0652.5155.0029.4745.2854.6113.5413.9410.7313.2413.3213.6812.43

695330252477252229296634373254

45.4648.9964.4270.6173.3239.0964.9474.5116.0316.3412.4015.3115.2815.8813.87

158

123

7468

66

15456

55

113

126

182

152

156

138

207

Fig 6. Segmentation results of the images in Fig 2 usingtwo-channel wavelet decomposition and reconstruction. Seg-mented calcifications from (A) original digitized image, (B)compressed reconstructed data with q = 512, and (C) com-pressed reconstructed data with q = 1,024.

Fig 5. Segmentation results of the images in Fig 1 usingtwo-channel wavelet decomposition and reconstruction. Seg-mented calcifications from (A) original digitized image, (B)compressed reconstructed data with q = 512, and (C) com-pressed reconstructed data with q = 1,024.

WAVELETS IN DIGITAL MAMMOGRAPHY35

ages. A solution to the latter can also be adifferent family of wavelets, currently underinvestigation, which would result in smootherimages with smaller gradient.

It should be pointed out that the Haar wave-lets used in this study are inherently nonsmoothcompression techniques and are expected to bediscontinuous across lines that run verticallyand horizontally. Thus, at very high compres-sion ratios, the artifacts introduced into thecompressed images consist of straight lines andcorners where these lines intersect. Usingsmoother wavelets would introduce differentartifacts. The Haar wavelets, however, have theadvantages that (1) they do not remove anysignificant infonnation pertaining to the calcifi-cation clusters as indicated by the unstructureddifference images between the original andcompressed reconstructed data and (2) theyintroduce artifacts that can be seen by theradiologist as totally artificial; indeed, therewere no false-positive readings of microcalcifica-tions by the radiologist on the compressedimages. In contrast, the wavelet segmentation

algorithm misread many of the edge artifacts asfalse-positive signals, which made some of thecompressed segmented images less useful to theradiologist as a tool for diagnosis. It remains tobe seen whether the advantages of smootherwavelets (no edges in the reconstructed images,fewer false-positive detections by the segmenta-tion algorithm) will outweigh the disadvantages(introducing artifacts that may be misread bythe radiologist as microcalcifications or other

structures).The results of the evaluation of the visualiza-

tion of the clustered calcifications are shown inFig 7 for the film, the uncompressed and the twosets of compressed data. In 60% of the films, thevisualization of the cluster is classified as excel-lent; in 13% the visualization of the clusters isvery good, and in 27% is good (Fig 7A). Thesame 60% and 13% of excellent and very goodcluster visualization respectively was obtainedfrom the digitized uncompressed images (Fig7B). However, only 8% were classified as goodwhile another 7% was classified as mediocre.The plots in Figs 7C and 7D show that the first

0

1

2 3 4c 5

Visualizalion 01 calcificationse 0 1 2 3 4 5

YlSUalizatioo of calcifications

6

Fig 7. Bar diagrams of theclassification of the visualizationof the calcifications in (A) the 15films, (B) the uncompressed digi-tized images, (C) the first set ofcompressed images, and (d) thesecond set of compressed im-

ages. The scale is 1, poor; 2,mediocre; 3, good; 4, very good,5, excellent.

0 1 2 3 4 5

Visualization of calcifications

8 0 1 2 3 4 5

Visualization of calcifications6

36 LUCIER ET AL

0 1 4 5 62 3

Degree of losses

0 1 2 3

Degree of losses

4 5 6

compression run with q = 128 or 512 demon-strates 47% excellent visualization for compres-sions up to 53:1, 20% very good, 13% good, and20% mediocre. The visualization degraded dur-ing the second compression run where thefollowing percentages were calculated from thecompleted answer sheets: 13% excellent forcompressions up to 56:1, 20% very good, 7%good, 33% mediocre, and 27% poor. It should benoted that the quality of the compressed datadepends on the image contents, namely theparenchymal density and the image noise.

The radiologist's estimates of the losses aftercompression led to the bar diagrams of Fig 8.Losses included artifacts not present in thefilms, changes in the morphology of the clusterand the individual calcifications, and distortionof the breast parenchyma. Assuming no lossesfor the films, the losses in the digitized mammo-grams and the compressed images are gradedon a scale of 1-5 from extreme to none. Scalenumber 3 corresponded to average losses andwas set as the limit of the visually acceptablelevel of losses for the purpose of this study.Figure 8B shows that only 13% of the first set ofcompressed images exceeded the average losses(grade number 3). Furthermore, the major con-tribution to this percentage was from the 10-bitimages. In contrast, 73% of the higher compres-sion results exceeded the average losses.

The analysis of the remainder of the expert'sevaluation indicates the following: (1) In 90% ofthe cases, the number of calcifications esti-mated within a cluster is the same between thefilm, the digitized mammogram, and the firstcompression set and falls one range lower forthe second compression set. (2) In 67% of thecases, the parenchyma density estimation andclassification remains the same between thefilm, the digitized images, and the first compres-sion set while a higher estimate is given for thesecond compression set. (3) In 33% of the cases,the same degree of suspiciousness of the lesionwas given from the film, the digital mammogramand the compressed images. However, in theremaining 67%, the compressed data gave theimpression of a less suspicious case than theoriginals. (4) The morphology of the calcifica-tions (shape, size, and geometry) degrades inthe entire second set of compression by one ortwo levels. Fifty-three percent of the first com-

0 1 2 3 4 5 6

Degree of losses

Fig 8. Bar diagrams of the grading of the overall losses in(AI the uncompressed digitized images, (B) the first set ofcompressed images, and (C) the second set of compressedimages. The scale is 1, extreme; 2, high; 3, average; 4, low; 5,none.

15

1413121110

9876543210

15

14131211

109876543210

15

1413121110

9876543210

pression data have similar morphology as thedigitized mammograms and the correspondingfilms; the remaining 47%, the majority of whichis from the 10-bit images, shows a one-leveldegradation in the morphology of the calcifica-tions. This also explains the differences in thesuspiciousness of the cluster. (5) The digitizedmammograms reproduce exactly the paren-chyma patterns observed on the film. In 33% ofthe cases, the first compression set did not showany visible distortion of the parenchymal tissues(the majority of these cases were from the groupof the 12-bit images). In all other cases thesmoothness and continuity of the parenchymaltissues is gradually lost and the compressed datahave a "boxy" appearance which increases withincreasing compression ratio.

to 56:1. Furthermore, the expert mammogra-pher could not discriminate the digitized fromthe decoded mammogram in 80% of the cases.However, the results seem to depend on thecontents of the original image and the dynamicrange of the digital mammogram. It also ap-pears that decoded images with higher dynamicranges were evaluated more favorably despitethe fact that the display of the images is limitedby the current technology to 8 bits per pixel.Further studies are needed if a digitizationstrategy more beneficial to the compressionprocess is to be determined.

A wavelet segmentation algorithm was alsoapplied to both uncompressed and compresseddata to determine whether it could partiallycompensate for the compression losses. Theresults showed that this algorithm, at its presentdesign, successfully segments the images butgenerates several false-positive signals in thehighly compressed data. Motivated by the re-sults of the present study, we are now engagedin the implementation of smoother waveletapproaches for the compression of mammo-grams and the improvement of the waveletsegmentation algorithm to reduce the false-positive detection rate which may, in turn,modify the clinically acceptable limits of lossycompression. A more extensive application ofwavelets to digital mammography including clini-cal evaluation and confirmation of our prelimi-nary results is ongoing.

CONCLUSIONS

We have applied Haar wavelets for the com-pression of mammographic images with calcifi-cation clusters aiming at the highest possiblecompression with clinically acceptable lossy data.Two high compression rates were tested todetermine the degree of losses and their effecton the visualization of malignant calcifications.The Haar wavelets introduced losses in thesmoothness and continuity of the pixels in theoriginal data but preserved the calcifications asindicated by the differences between the origi-nal and compressed images and the fact that thevisualization of the calcifications was rated asexcellent by the radiologist for compressions up

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38 LUCIER ET AL

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