Evaluation of Penalty Design in Penalized Maximum- likelihood Image Reconstruction for Lesion Detection

Transcription

1 Evaluation of Penalty Design in Penalized Maximum- likelihood Image Reconstruction for Lesion Detection Li Yang, Andrea Ferrero, Rosalie J. Hagge, Ramsey D. Badawi, and Jinyi Qi Supported by NIBIB under grant no. R01EB B I O M E D I C A L E N G I N E E R I N G

2 Introduction PET is widely used in oncology Increasingly being used for staging and treatment monitoring Challenging to detect small tumors (< 10 mm) Numerous efforts have been focused on improving detection of small tumors by developing New PET tracers New PET scanners: time- of- flight, dedicated systems, etc. Optimized image reconstruction methods (our focus)

3 PML Image Reconstruction PML image reconstruction ˆx(y) = arg max[l(y x) (x)] x 0 Quadratic penalty function (x) = Shift- invariant penalty kernel NX j=1 X ln j jl(x j x l ) = x t Rx Rx =Ker R (m, n, o) x(m, n, o) D 1 st order quadratic penalty 4 Ker R Parameterization (Stayman et al 000) Ker R = X l Penalty design: to find the optimal lb l = b 1 b

4 Optimize Penalty Function Quadratic penalty function has been optimized for: Achieve uniform resolution Optimize local contrast to noise ratio Improve lesion detectability in D (Stayman et al 000, 004, Qi 000) (Qi 1999) (Qi et al 006, Yang et al 01) In the previous work [1], we have designed the penalty function to improve the lesion detectability in 3D image, and validated it using computer simulations Goal: to evaluate the proposed penalty function for lesion detection using real data [1] Yang et al, 014, PMB,

5 Lesion Detection To study lesion detectability, numerical observers are often used è Normal (H0) è Abnormal (H1) Human Observer Figure of merit (FOM) Numerical Observer 1 ROC CURVE TP AUC Popular numerical observers: D: channelized Hotelling observer (CHO) 0 1 FP (Yao and Barrett 199) 3D: single- slice CHO, volumetric CHO, multislice CHO, multislice multiview CHO, multiview CHO ( Liang et al 008, Kim et al 004, Platisa et al 011, Chen et al 00, Gifford et al 006) 5

6 Multiview CHO D channels 3D image ˆx Channel outputs U ˆx 1 3 FOM : SNR = z 0 U 0 K 1 Uz Internal noise n with zero mean and covariance K n Test statistics z 0 U 0 K 1 ( ) U ˆx + n ( : mean reconstructed lesion profile) Hotelling Observer U ˆx + n 6

7 Multiview CHO SNR of PML FOM: SNR = z 0 U 0 K 1 Uz For lesion at a given location, SNR of PML reconstruction can be evaluated by using locally shift invariant approximation: (Qi 004) where 8 8 >< { Ũ 8 >< i } i=1 { { i } >: N i=1 > 8 >< >< { i } N i=1 {{µ >: i } N i=1 >: : the Fourier transform of the channels : the Fourier transform of the column vector of the Fisher information matrix corresponding to the lesion location : the Fourier transform of the expected lesion profile : the Fourier transform of the penalty kernel 7

8 Penalty Design Objective: to maximize for every voxel 1 st order quadratic penalty: b 1 = , and b = Equivalent to finding the optimum weights γ : ˆ = arg max SNR ( ) We used 9 nearest neighboring voxels ( ) in 3D To reduce computational cost, the penalty weights were computed for a subset of preselected voxels and the nearest neighbor interpolation was used to form the overall penalty function 8

9 Patient Background Data We used a 60- minute dynamic PET scan of a female patient on a GE DST whole- body PET scanner 5 mci FDG injection FOV: 700 mm (transaxial) x 157 mm (axial) Crystals size: 6.54 x 6.54 x 30 mm The FOV covered the heart, breasts, and part of the lungs and liver The last 45 minutes data were summed to create a high- count sinogram with ~800M events (9 of a normal scan) The reconstructed patient image was verified by a radiologist to be free of lesion and the sinogram data were used as the noise- free normal background 9

10 Lesion- Present Data A Na- point source was scanned in air at 7 locations Attenuated by the patient body Added to the patient sinogram 7 implausible positions were excluded Sample reconstruction with a superimposed lesion in the liver Independent Poisson noise was introduced to generate 00 independent noisy realizations, each with around 90M total counts, mimicking a 5- minute scan 10

11 Image Reconstruction Image matrix size: 19 x 19 x 47 Voxel size: 3.64 x 3.64 x 3.7 mm Randoms, scatters, and normalization factors were estimated from the patient data using a manufacturer provided software and included in the reconstruction Reconstruction algorithm: PML with the 1 st order quadratic penalty PML with the optimized penalty Both reconstruction methods used the same forward/back projectors and correction factors 11

12 Detection Performance Lesion detectability of PML reconstructions at two representative locations Proposed penalty 1.8 Location 1 SNR st order quadratic penalty log10( ) 1.8 Location SNR log10( ) SNR of theoretical (curves) and Monte Carlo results ( x & o ) 1

13 Human Observer One human observer was asked to perform AFC experiment The resulting percent correct (PC) can be converted to SNR: (Burgess 1995) SNR at two representative locations: Location 1 Location Proposed penalty SNR 1 SNR st order quadratic penalty log10( ) log10( ) SNR of theoretical (curves) and human observer results ( x & o ) 13

14 Human Observer AFC Results The β value of the 1 st order penalty was tuned for each tumor individually The optimized penalty improves the SNR by up to 15%.5 Maximum SNR Optimal penalty 1st order quadratic Tumor # 14

15 Statistical Test Each AFC experiment was considered as a Bernoulli experiment with possible outcomes Sort the AFC results of two penalty functions into 4 categories 1 st order penalty Proposed penalty Number of cases 1 Correct Correct N 1 = 991 Wrong Wrong N = 56 3 Correct Wrong N 3 = Wrong Correct N 4 = 14 Under the null hypothesis, categories 3 and 4 should happen with same probability (N3 N4) Using the McNemar test, we obtained a p- value <

16 Summary We designed the penalty function in PML image reconstruction for 3D lesion detection, and evaluated the detection performance using real data Both numerical and human observer results show that the proposed penalty outperforms the 1 st order quadratic penalty In the future we will investigate the dynamic PET for lesion detection 16

17 Thank you!