Wavelet-based Denoising of Cardiac PET Data

M.A.Sc. Thesis

Geoffrey Green, B. Eng.(Electrical)

Supervisors:• Dr. Aysegul Cuhadar (Carleton SCE)• Dr. Rob deKemp (Cardiac PET Center, Ottawa Heart Institute)

January 11, 2005

Outline of Presentation Problem Statement / Thesis Motivation Thesis Objective Thesis Contributions / Publications Background Information

Cardiac anatomy PET and its use in cardiology Wavelets and wavelet-based denoising

Spatially Adaptive Thresholding Cross Scale Regularization Denoising Experiments Representative Results Future Work

Problem Statement / Thesis Motivation (1)

PET images of the heart using 82Rb radiotracer are performed to observe and quantify uptake of blood flow to the heart muscle.

Such myocardial perfusion measures can be used to diagnose coronary arterial disease and prescribe an appropriate treatment.

82Rb is used for several practical reasons: no on-site cyclotron required short half life (76s) allows quick, repeated studies like potassium, selectively taken up in cardiac muscle tissue

HOWEVER, the PET data that results from 82Rb is highly contaminated by noise, leading to erroneous uptake images and extracted physiological parameters that are biased.

Problem Statement / Thesis Motivation (2) Clinical noise reduction protocol used at OHI involves filtering

with a fixed-width Gaussian kernel, regardless of noise level.

This method is not adaptive to images of differing quality, and tends to oversmooth smaller-scale image features.

More effective noise suppression techniques would lead to more accurate images, and a subsequent decrease in the risk of misdiagnosis and inappropriate treatment.

RAW DATA GAUSSIAN FILTERED

myocardium

Published Results

G. Green, A. Cuhadar, and R.A. deKemp. Spatially adaptive wavelet thresholding of rubidium-82 cardiac PET images. In EMBC 2004: Proceedings of the 26th International Conference, IEEE Engineering in Medicine and Biology Society, San Francisco, CA, USA, pages 1605-1608, 2004.

Thesis Objective

“The goal of this thesis is to develop denoising methods that improve the quality of cardiac 82Rb PET scans, and illustrate their effectiveness and robustness when used to measure myocardial perfusion.”

The methods we investigate are based on the current state of the art denoising methods using a wavelet representation. It is well-established in the literature that wavelet-based denoising can outperform Gaussian LPF methods, separating signal from noise at multiple image scales.

Thesis Contributions We apply the following recently-developed wavelet denoising

techniques to cardiac 82Rb PET data: spatially adaptive (SA) thresholding cross-scale regularization (CSR)

We investigate the relative effect that these methods have on the denoised result when they are applied:

individually (across multiple scales), in combination (across multiple scales), and to various image domains (2D and 3D)

We propose a novel denoising protocol that comprises a hybrid of the above methods, and illustrate the improvement it offers when compared to the current clinical protocol.

Background - Cardiac Anatomy

myocardium

blood pool(cavity)

apex

The left ventricle is modelled as a semi-ellipsoid, containing a muscular wall (myocardium) which surrounds a blood pool.

When viewed from the apex along the axis of the ellipsoid, the myocardium appears as a ring.

Forceful contraction of LV is vital for blood supply to body.

slices

Background - PET Used to observe and measure physiological

processes in vivo.

Patient is injected with a radioactive tracer, which is selectively taken up (in myocardium).

As tracer nucleus decays, a positron is emitted and travels a short distance (~mm) before colliding with an electron from a nearby atom, causing an annihilation

This creates two 511keV gamma rays that are emitted at ~180o, picked up by external detectors

Image reconstruction algorithms form a spatial representation of tracer distribution, using either:

- filtered backprojection (FBP), or - ordered subset expectation maximization (OSEM)

Background – PET in cardiology Used for both qualitative (location of defect) and quantitative analysis

Performed under rest and stress conditions

Quantitative analysis uses a time series of images (frames), extracted TACs as input into a compartmental model

Nonlinear regression used to determine model parameters (e.g. K1) from measured PET data

QualitativeQuantitative

reduced uptake in damaged area

Myocardial cellsM(t)K1 K2

InputFunction

polar map TAC

compartmental model

Background – Wavelets (1)

Very active research area during the last 10 years

Wavelets provide an inherent advantage when denoising non-stationary signals, such as those found in cardiac PET imaging - the inclusion of localized “fine scale” functions in the basis allows one to better discern diagnostically significant details

The DWT is a signal representation whose members consist of shifted, dilated versions of a chosen basis function

The DWT is realized efficiently with an iterated filter bank, generating subbands of coefficients

Background – Wavelets (2)

Filter bank implementation of wavelet transform

Detail coefficients

d=1 d=2 Level

2

1

3

Approx.coeffs

Detail coefficients

d=1 d=2 Level

2

1

3

Approx.coeffs

Background – Wavelet based denoising

Noisy Image

Noisy DWT

coefficientsForwardWT

InverseWT

Denoised DWT

coefficients

Denoised ImageWavelet Wavelet

CoefficientCoefficientThresholdingThresholding

Overall denoising process:

A multidimensional DWT which is meant to exploit the correlation within/between image slices

Wavelet basis (3D discrete dyadic wavelet transform -Koren/Laine,1997) based on splines, which are well-suited to this class of images

A translation-invariant wavelet representation, which reduces ringing effects in the reconstructed image

The assumption is an The assumption is an additive Gaussian noise modeladditive Gaussian noise model

Spatially Adaptive Thresholding Technique introduced by Chang,Yu,Vetterli (2000)

Attempts to distinguish features from background in wavelet domain, and adjusts threshold T[k] accordingly. This is done by computing the local variance of the DWT coefficients, W[k]:

Feature area (e.g. edge) – coefficient variance large, threshold set low in order to retain feature unchanged

Background area – coefficient variance small, threshold set high in order to suppress (noticeable) noise in that area

][][

2

kkT

W

n

Spatially Adaptive Thresholding – 1D example

Spatially Adaptive Thresholding – 1D example

Cross Scale Regularization

Technique introduced by Jin, Angelini, Esser, Laine (2002)

In the case of high noise levels (as in 82Rb PET), the most detailed subbands (i.e. level 1 coefficients) are usually dominated by noise which cannot be easily removed using traditional thresholding schemes

To address this issue, a scheme is proposed that takes into account cross-scale coherence of structured signals.

The presence of strong image features produces large coefficients across multiple scales, so the edges in the higher level subbands (less contaminated by noise) are used as a “oracle” to select the location of important level 1 details.

Wavelet modulus of coefficients at the next most detailed subband (i.e. level 2) is used as a scaling factor for the level 1 coefficients.

Cross Scale Regularization – 1D example

Denoising Experiments

PhantomPhantom Input Data (since Input Data (since a prioria priori tracer info is unknown) tracer info is unknown)

healthy, short-axis oriented sliceshealthy, short-axis oriented slices simulated PET noise of varying types (merge phantom with simulated PET noise of varying types (merge phantom with clinical image that has no features present)clinical image that has no features present)

ClinicalClinical Input Data (supplied by OHI) Input Data (supplied by OHI)

healthy, short-axis oriented sliceshealthy, short-axis oriented slices Static: OSEM/FBP reconstruction, stress/rest studyStatic: OSEM/FBP reconstruction, stress/rest study Dynamic: OSEM reconstruction, stress/rest studyDynamic: OSEM reconstruction, stress/rest study

Denoising Experiments

The denoising protocols require an estimate of noise variance The denoising protocols require an estimate of noise variance in the image. Robust median estimator allows a in the image. Robust median estimator allows a data-drivendata-driven estimate from the noisy wavelet coefficients:estimate from the noisy wavelet coefficients:

6745.0/]))[((Median 1 kMabsn

We investigate a set of 17 denoising protocols in order to We investigate a set of 17 denoising protocols in order to assess the effect of using SA/CSR techniques:assess the effect of using SA/CSR techniques:

when applied to multiple decomposition levels independently, when applied to multiple decomposition levels independently, when applied to multiple decomposition levels in combinationwhen applied to multiple decomposition levels in combination when applied in various domains (2D vs. 3D)when applied in various domains (2D vs. 3D)

Denoising Experiments Figures of MeritFigures of Merit

Phantom DataPhantom Data MSEMSE Visual AssessmentVisual Assessment

Clinical DataClinical Data Visual Assessment - Visual Assessment - STATIC studySTATIC study Coefficient of Determination (RCoefficient of Determination (R22) - ) - DYNAMIC studyDYNAMIC study Normalized KNormalized K11 std. dev. - std. dev. - DYNAMIC studyDYNAMIC study

Selected Results - PhantomMSE vs. Denoising Protocol for 3D Phantom Image

Gaussian

Selected Results – Static Clinical Data

Denoised Images – 3D denoising, OSEM stress study

SA @ level 3,CSR @ level 2

SA @ level 3,CSR @ level 2,1

Selected Results – Dynamic Clinical Data

Model outputs vs. Denoising Protocol - 3D, OSEM stress

Future Work Development of a more sophisticated noise model

Applicability to higher dimensions (including time) – 4D, dynamic polar map

Investigate denoising in sinogram domain

Alternate signal basis (e.g. platelets, brushlets, curvelets)

Application to other PET studies (e.g. ECG-gated, NH3 tracer)

Statistical significance testing

Denoising GUI In order to facilitate the investigation of parameter changes on In order to facilitate the investigation of parameter changes on

the denoised results, a GUI was implemented.the denoised results, a GUI was implemented.

Wavelet-based Denoising of Cardiac PET Data

M.A.Sc. ThesisGeoffrey Green, B. Eng.(Electrical)

Supervisors:• Dr. Aysegul Cuhadar (Carleton SCE)• Dr. Rob deKemp (Cardiac PET Center, Ottawa Heart Institute)

January 11, 2005

Quantitative Results

Quantitative Results

Detail coefficients

d=1 d=2

Approx.coeffs Level

2

1

3