Diagnostic Compression of Biomedical Volumes

VOLUMES

Alberto Signoroni, Riccardo Leonardi

Signals and Communications Lab., Dept. of Electronic forAutomation,

University of Brescia,

via Branze 38, I-25123 Brescia, ITALY

Tel: +390303715432;fax: +39030 380014

e-mail: signoron,leon@ing.unibs.it

ABSTRACT

Inthisworkwedealwithlossycompressionof

biomedi-calvolumes. Byforceofcircumstances,diagnostic

com-pressionis bound to asubjective judgment. However,

withrespecttothealgorithms,thereisaneedtoshape

thecodingmethodologysoastohighlightbeyond

com-pressionthreeimportantfactors: themedicaldata,the

specic usage and the particular end-user. Biomedical

volumes may have very dierent characteristics which

derivefrom imaging modality, resolution and voxel

as-pect ratio. Moreover,volumes are usually viewedslice

bysliceonalightbox,accordingtodierentcutting

di-rection(typicallyoneofthe threevoxelaxes). Wewill

see why and how these aspects impact on the choice

ofthe coding algorithm and onapossibleextension of

2Dwellknownalgorithmstomoreecient3Dversions.

Crosscorrelationbetween reconstruction error and

sig-nalis akeyaspect to keepinto account;we suggestto

applyanonuniformquantizationtowaveletcoecients

in order to reduce slicePSNRvariation. Once agood

neutral coding for a certain volume is obtained, non

uniformquantizationcanalsobemadespacevariantin

ordertoreachmoreobjectivequalityonVolumesof

Di-agnosticInterest(VoDI),whichin turnscandetermine

thediagnosticqualityoftheentiredataset.

1 INTRODUCTION

Intheeld of biomedicalsignalcompression there isa

strongrequirementoferrorlessreconstruction. This

de-rives from dierent and apparent obvious motivations,

mostimportantly to overcomelegal and diagnostic

is-sues. However, even in its most eective

implementa-tions,lossless compression cannotovercomeadata

de-pendent[1]compressionfactorwhichremaintoolowfor

ecientstorageand transmissionin avariety ofPACS

[2] application contexts. By the way, diagnostic

cod-inghasbeenintroduced inthecaseofimagecoding[3]

and itis based on thediagnostic quality denition: a

lossyreconstructedbiomedicalvolumecanbeaccepted

from a diagnostic quality point of view, if aphysician

withsamequalicationlevelcanestablishthesame

di-informationenclosed)withrespectto theoriginalone.

Inthiswork,awaveletbasedapproachisconsideredin

thecaseofvolumetriccompression,usingMRIandCT

anatomical data (Sec.2). Volumetric compressed

ma-terial may exhibit peculiar artifacts depending on the

visualization strategy mainly because of signal to

er-ror crosscorrelation. This must be taken into account

to improve on the coding scheme. In Sec.3 an

anal-ysis of these sorts of artefacts is carried out. Let us

stress that in the present JPEG2000 standardization

process, even if biomedical imaging is considered, 3D

codingisnotdirectlyaddressedandthecodingstrategy

doesnottakeintoaccounttheimplicationsoftheabove

concern. Moreover,videocodingimplements2D+t

pre-dictivemotionorientedcodingschemeswithparadigms

that we cannot consider adequate for static volumes,

giventhelackofmovingobjects.

2 3D WAVELETCODING

Zerotree-waveletcoding[4,5],withallitsvariants,

cur-rentlyrepresentsone of thethe mostecientwaysfor

progressive image compression, with the possibility to

embedlossyandlosslesscodinginaunique

multiresolu-tionframework. Progressivecodingisessentialfor

com-municatingandarchivingimages andvolumes. This is

due to the possibility to rene, even in a spatially

lo-calized fashion, or to erodethe compressed bit-stream

withouthavingtorecodetheentiredata. CTandMRI

volumetricscansproduceaset ofsamples(voxels)ona

3D grid (usually regular but not necessarilyisotropic)

and quantize themonagraylevelscalewithne

gran-ularity(usually 12bit/voxelstored usinga16 bit short

integer)but with arelativelylowSNR [1]. The

poten-tial of a 3D extension of zerotree schemes has already

beenpresentedbysomeauthors[6,7]. Inorder tohave

a perfect reconstruction, it is necessary to perform an

integer-to-integerwavelettransform(WT),butin

prac-tice it is uselessto spend bit to reconstruct thesignal

below its source noise variance. Integer WT may be

usedtolowerthecomputationalcost,butoatingpoint

opti-Original

3d coded

0.232 bpp

2d coded

0.232 bpp

Figure1: Dierentresultsfor3D(PSNR=37dB)andrepeated2D(z) coding(32.5dB)at thesameCR=52.

afterquantization. Forexampleaproductmaskmaybe

appliedto the waveletcoecients to highlightRegions

orVolumes of DiagnosticInterest(RoDI [3], VoDI) or

toperformanon-uniformquantizationofsubbands.

2.1 The Voxel anisotropy problem

Forthegreaterpartofimagingmodalities,thespectral

characteristicsofeachslicefollowthetypical1/f model

fornaturalimageswell,whereasagoodmatchwiththe

1/f model along thethird dimension stronglydepends

onthe voxel resolution anisotropy with respect to the

isotropiccube. Inotherwords,someenergycompaction

deciencies of the WT along the z dimension may

oc-curdue tothetypicallowerresolution intheslicing

di-rection. This may compromise the zerotree algorithm

performance due to a breakdown of the 1/f spectral

characteristics. We will highlight, giving an example,

thedependencies of3D wavelet coding with respect to

the image source and z-resolution. As a reference we

compare 3D coding performance over that of a set of

repeated2Dones.

2.2 3Dcodinggain over repeated 2D

InTab.1,acomparisonofcodingperformanceisshown

between two dierent imaging data sets, i.e. a

CT-abdomen and a MRI-brain (256x256)x128 slice sets,

which has been subsampled to obtain dierent

z-resolutiondatasets (128and64slices). Theinitialdata

sets havebeen produced with anisotropicvoxelsof

re-spectively2x2x4mmand0.78x0.78x1.17mmspatial

res-olution. As for the decomposition, we use the set of

biorthogonal lters proposed in [4]. The 3D

separa-ble WT decomposition is performed with 5 levels for

128slices dataset and with 4 levels for the 64 resliced

ones. Itis reasonableto consider onlyaseparableWT

implementationforcomputationaleciency,and

dier-entbasis alongeachdimension, in orderto betterdeal

with anisotropy of the voxel characteristics. As

cod-ingalgorithmweperformSPIHT[5]codingrepeatedon

each slice and a 3D version of SPIHT. The total

bit-tortion are used to compare the resulting compression

ratios(CR=12bpp/stream-bpp). HerethePSNRvalue

of 45dB represents an absolute visually lossless

qual-ity,evenifreconstructedimagesaremagniedand

com-pared athigh zoomfactors. Aswecannotice, theCR

%gain ofthe3D algorithmoverthe 2D(z)algorithm is

moreimportantfortheCTdataset. Ontheotherhand,

forthesubsampled64sliceMRIthereisonlyalittlegain

inusingthe3Dcodingapproach. Usually,MRIdataare

moredetailed and noisywithrespectto CTones,thus

theWTdoesnotallowagooddecorrelationwhilehigh

predictivity of coecients(by zerotree)in the z

direc-tionisweakened. InFig.1,weshowanexampleof2D(z)

and 3D coding results for the slice40 of CTdata set.

Forlowz resolution datasets it is sometimes better to

use shorter lters in the z direction, such as the haar

basis[6]. An alternativeistochangethewavelet

repre-sentationinordertodesignapredictivecodingschemes

along z. This is an open research area, because it is

important, given the imaging modality and the voxel

aspectratio andresolution, to nd anoptimal wavelet

representation in terms ofcoding eciency. Moreover,

there are other issuesthat mustbetaken into account

in ordertoenvisageadiagnosticcompression.

3 VOLUMETRICCODING ERRORS

Itiswellknownthatthereconstructionerror

autocorre-lation and theerrortosignalcross-correlationdepends

onthedecompositionstructure,thequantizationmodel

andthereconstructionltershape. Aquantitative

anal-ysis ofthe phenomenais outof thescopeof this short

contribution, but we want to summarize some

deriva-tionsofthistypeofanalysisinaqualitativemanner.

A 2D(z) coding strategyhasthe advantageof

allow-ingaprecisePSNRcontrolovereachsingleslice,as

de-picted in theaboveexperiment andshown in Fig.3(a);

in the 3Dcasethis is notguaranteed due to the

quan-tizationprocess usedinthezerotreecoding, andtothe

spreading of quantization error in a localized fashion

advan-3d coded CR=34.2

2d(z) coded CR=25.7

original |/ resliced target D

35 dB

target D

35 dB

Figure2: MRIslices originatedbyavolumereslicing ony. ForboththecodingmodalitiesatargetdistortionPSNR

of35dBwasused,but somestreakingartifacts,dueto errorz-uncorrelation,areevidentontherightmostimage.

Data CT CT MRI MRI

128 64 128 64 2D 3D/g 2D 3D/g 2D 3D/g 2D 3D/g D(dB) CR > 45 7.8 14.3 7.5 9.3 5.5 5.7 5.5 5.5 83% 24% 4% 0% 40 14.1 30.7 13.7 18.4 9.3 9.6 9.2 9.1 118% 34% 3% -1% 37 20.8 53.1 19.9 29.3 16.2 18.2 16.0 16.1 155% 47% 12% 0.6% 35 28.5 74.4 26.9 43.9 25.8 31.9 25.2 26.0 161% 63% 24% 3.2%

Table1: Comparisonbetween2D(z) and3Dcodingon

dierentdatasets. Foreachdatasetandforeachtarget

PSNR distortion D (dB), repeated 2D and 3D coding

areperformed,andthecompressionratio(CR)andCR

%gain(g)of3Dover2D(z)isquoted.

consideronly thezslicingdirection fordiagnostic

pur-poses. He/she canuse any cutting plane, for example

followingthexoryaxes. Fig.3(b)showsthe2DPSNR

vs y-slice number in an interval taken from the same

datasetof Fig.3(a). From aperceptual point of view,

the artifactscaused by 3D coding are always

defocus-ing and eventuallyringing (depending on the CR, the

cutdirectionvsvoxelanisotropy,thezoomingfactor...);

in other words,these artefacts are correlated with the

signalcharacteristics. Inthe2Dcase,instead,the

quan-tizationmayintroduceobjectionable errorsalongthez

dimension,becausethereconstructedsignallacks

corre-lationinsuchdirection. Thisdeterminesuncontrollable

mismatchwhich,atmediumorlowbitrates,mayalter

theanatomicalstructuresinthedataset,ascanbeseen

inFig.2.

3.1 PSNRconstancy

Fig.3(a,b) show a regular oscillation of the per-slice

lationisshapedbythequantizationinverseWTerrorof

therstlevelwaveletcoecients(higherfreq.). Despite

thelocalized PSNRcontrolonzslicefor2D(z)coding,

the PSNRoscillationwithrespect toother slicingaxes

is nearly thesame for both coders(Fig.3(b)). This

su-perposition is due to the intrinsic separable nature of

embedded wavelet coding which is robustwith respect

toPSNRcontrolinonedirection.Beingtheslicesat

ad-jacentpositionquitesimilaronetotheother,thePSNR

variationmaybeperceivedonthescreen lightboxeven

atmedium-lowrates,causingobjectionableartifactsand

loweringthereliabilityofthecoding. Itisimportantto

nd some methodology to lower the amplitude of the

oscillation. Weproposetooperateanonuniform

quan-tizationontherststagesofwaveletcoecients.

3.2 Non-uniformquantization

In Fig.3(c) three curvesare shown representingthe

ef-fect of twoWT coecient levelweighting.

Multiplica-tiveweightareappliedpriortoSPIHTquantizationand

taken o prior to inverse WT. The measurements are

performedat thesameCR.It iseasy tosee the

imme-diate benet in terms of PSNR oscillations, while the

global PSNR performanceget slightly worse, as itcan

beexpected. Resultsonzslicingdirectionsreectswhat

happens in theother direction aswell. Theoscillation

standarddeviationintheoriginalcaseis0.4dB,while

weightingtherstWTlevelbyafactorof2,thedrop

to0.2dB,andwith1stWTlevelweight,WTlw=4and

2ndWTlw=2,=0.13dB.Thiskindofmasking isin

accordance with the results of perceptual studies

aim-ingtoobtainagoodmatchbetweensubbandweighting

andHVScharacteristics. Acombinedstudyshouldgive

optimalresults. Thus,evenifglobalPSNRworsensthis

doesnotimplyaworseimagequality. Itisalso

interest-ing to note how the PSNR oscillationpattern changes

ifwereducequantizationerrorsforexampleintherst

WTlevel. InFig.3(d)weapplytwomasks: M1consists

cod-ment is performed on each WT coecient. With M2

the 1st level coecients are best represented (12

bit-planesWTprecision)butthePSNRoscillationpattern

isnowdominatedfromhigherlevelcoecients. Itis

in-terestingtoseehowwithM1wetakeadvantageofa

fa-vorableintermediatesituation betweenthe unweighted

coding pattern ( = 0.30dB) and what corresponds

to M2 ( = 0.50dB). With M1 we obtain a PSNR

=0.17dB.

4 CONCLUSION

Inthis presentation we haveseenthat 2D(z) coding is

notwell suited for compression of biomedical volumes

because it is less ecient with respect to 3D coding

and it allows a distortion control only along z while

presenting PSNR inter-slice oscillations as well as

po-tential objectionable artifact considering other slicing

directions. We haveproposed 3D SPIHT coding with

nonuniformquantizationofsubbandsinordertoreduce

PSNRoscillationsforeveryslicingdirections. Good

re-sults havebeen obtainedwithout impairing subjective

quality(whichcanbecomeevenbetterfromaperceptual

pointofview). All this,withagoodwavelet

decompo-sition, must be done ona given image modality, voxel

aspectratioandresolution,toguaranteeanecientand

reliablecompressionofbiomedicalvolumesthatcanbe

thebasisfordiagnosticcoding.

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upper: 3d 1st WTlw=4 (D=40.9dB,CR=6.6)

middle: 3d 1st WTlw=2 (D=37.7dB,CR=13)

lower: 3d (D=34.9dB,CR=32)

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slice nr. Z

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MRI 3d coding with subband masking − 10 bit−planes on WT

3d (D=40dB)

3d 1st WT level weight=2

3d 1st WTlw=4, 2nd WTlw=2

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slice nr. Z

PSNR (dB)

MRI 3d coding with subband masking (same CR=9.6)

2d(z) (Z−slice D=40dB, CR=9.3)

3d (D=40dB, CR=9.6)

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39

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slice nr. Y

PSNR (dB)

MRI brain 2d(z) vs 3d coding: Y−slice PSNR

2d(z) (Z−slice D=40dB, CR=9.3)

3d (D=40dB, CR=9.6)

20

40

60

80

100

120

39

40

41

slice nr. Z

PSNR (dB)

MRI brain 2d(z) vs 3d coding: Z−slice PSNR

(a)

(b)

(c)

(d)

Figure3:PSNRperformancecomparisonbetween2D(z)

and3Dcoding(a),(b)anddierentweightingofwavelet