Wavelet-based Denoising of Cardiac PET Data

1. 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

2. 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

3. Problem Statement / Thesis Motivation (1) • PET images of the heart using 82Rb radiotracer are performed to observeand 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.

4. 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. Problem Statement / Thesis Motivation (2) RAW DATA GAUSSIAN FILTERED myocardium

5. 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.

6. 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.

7. 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. Thesis Contributions

8. blood pool (cavity) Background - Cardiac Anatomy myocardium slices 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.

9. 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

10. Used for both qualitative (location of defect) and quantitative analysis Background – PET in cardiology Quantitative Qualitative polar map TAC Input Function reduced uptake in damaged area Myocardial cells M(t) K1 K2 compartmental model • 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

11. 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 (1)

12. Background – Wavelets (2) Filter bank implementation of wavelet transform

13. Approx. coeffs Detail coefficients d=1 d=2 Level 1 2 3

14. Approx. coeffs Detail coefficients d=1 d=2 Level 1 2 3

15. Overall denoising process: Background – Wavelet based denoising Noisy DWT coefficients Denoised DWT coefficients Noisy Image Denoised Image Inverse WT Forward WT Wavelet Coefficient Thresholding • 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 additive Gaussian noise model

16. 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, sW[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

17. Spatially Adaptive Thresholding – 1D example

18. Spatially Adaptive Thresholding – 1D example

19. 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.

20. Cross Scale Regularization – 1D example

21. Denoising Experiments • Phantom Input Data (since a priori tracer info is unknown) • healthy, short-axis oriented slices • simulated PET noise of varying types (merge phantom with clinical image that has no features present) • Clinical Input Data (supplied by OHI) • healthy, short-axis oriented slices • Static: OSEM/FBP reconstruction, stress/rest study • Dynamic: OSEM reconstruction, stress/rest study

22. Denoising Experiments • We investigate a set of 17 denoising protocols in order to assess the effect of using SA/CSR techniques: • when applied to multiple decomposition levels independently, • when applied to multiple decomposition levels in combination • when applied in various domains (2D vs. 3D) • The denoising protocols require an estimate of noise variance in the image. Robust median estimator allows a data-driven estimate from the noisy wavelet coefficients:

23. Denoising Experiments • Figures of Merit • Phantom Data • MSE • Visual Assessment • Clinical Data • Visual Assessment - STATIC study • Coefficient of Determination (R2) - DYNAMIC study • Normalized K1 std. dev. - DYNAMIC study

24. Selected Results - Phantom MSE vs. Denoising Protocol for 3D Phantom Image Gaussian

25. 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

26. Selected Results – Dynamic Clinical Data Model outputs vs. Denoising Protocol - 3D, OSEM stress

27. 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

28. Denoising GUI • In order to facilitate the investigation of parameter changes on the denoised results, a GUI was implemented.

29. 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

30. Quantitative Results

31. Quantitative Results

32. Approx. coeffs Detail coefficients d=1 d=2 Level 1 2 3