GPU implementation for rapid iterative image reconstruction algorithm

Transcription

1 GPU implementation for rapid iterative image reconstruction algorithm and its applications in nuclear medicine Jakub Pietrzak Krzysztof Kacperski Department of Medical Physics, Maria Skłodowska-Curie Memorial Cancer Center - Institute of Oncology, Warsaw, Poland Institute of Experimental Physics, Faculty of Physics, University of Warsaw

2 Outline Single Photon Emission Tomography Why do we need more computational power? Our software Results and efficiency comparison

3 Outline Single Photon Emission Tomography Why do we need more computational power? Our software Results and efficiency comparison

4 Single Photon Emission Tomography (SPECT) Emission Tomography, Miles N. Wernick and John N. Aarsvold

5 Single Photon Emission Tomography (SPECT) Detector Gamma emission Radioisotope

6 SPECT SPECT / CT Radiation source inside the patient, functional images of metabolic processes. CT Radiation source outside the patient, structure of body organs, (attenuation coefficient). 123 I-MIBG SPECT CT SPECT/CT

7 Single Photon Emission Tomography (SPECT) series of 100 projections 3d reconstructed data

8 Single Photon Emission Tomography (SPECT) 3d reconstructed data

9 Two approaches to image reconstruction : Analytical methods FBP fast but approximate Statistical (iterative) Reconstruction MLEM accurate but more computational power needed s y l p(f,s) g f f(x,y) x M f f(x,y) 2 0 F 1 1, f) P( df

10 Why Statistical Iterative Reconstruction? SPECT: Phantom OSEM, 30 subs., 2 iter. FBP OSEM, 30 subs., 20 iter.

11 Why Statistical Iterative Reconstruction? The application of iterative reconstruction methods in SPECT allows to reduce the time of data acquisition process (for instance from 30 to 15 minutes). Reduce the radiation dose, Enable to use more sophisticated hardware (modeling of hardware physics) HR collimator, 25 min. with RR, FBP MR collimator (3.5 HR), 10 min. with RR, 48 iter.

12 Outline Single Photon Emission Tomography Why do we need more computational power? Our software Results and efficiency comparison

13 Taking a single projection. Geometric collimator response function detector M g g = Mf f Septal penetration, scatter,

14 Numerical complexity of the full iterative reconstruction Typical problem size: Spatial resulution of SPECT: ~1cm, Pixel size: 4-8 mm, Typical reconstruction matrix size: , Number of image voxels: ~10 6 (4 byte values), Number of iterations: from 20 to 1000, Number of non-zero elements of M: ~ (r/w operations) several hours on standard PC!

15 Numerical operations (rotation based projector) 1. rotation 2. Gaussian blur 3. projection.. and aritmethic matrix operations

16 Start Image Reconstruction Projector Rotation Gaussian blur Image estimate Projection with attenuation More iterati ons? Reconstructed Image Image estimate update Backprojection estimated Compare? = measured Measured data

17 Rotator Bilinear (inverse mapping) Gaussian ( forward mapping ) An Optimal Rotator for Iterative Reconstruction, Jerold W. Wallis and Tom R. Miller

18 Why do we use CUDA? Projection operator is simple to parallelize, values of projection pixels can be computed independently at the same time, Fast floating point mathematical functions and cashed arrays can speed up the projection, correction and filtering processes, Linear Texture Interpolation (used in rotations),

19 Outline Single Photon Emission Tomography, Why do we need more computational power? Our software Results and efficiency comparison.

20 Our software Complete simulator of the SPECT scanner modeling the physics of emission tomography (xspect scanner), Image reconstruction module (xspect reconstructor), Two versions of the software: GPU and CPU only.

21 xspect scanner

22 xspect reconstructor

23 Reconstruction (1)

24 Reconstruction (2)

25 Reconstruction (4)

26 Reconstruction (8)

27 econstruction (16)

28 econstruction (32)

29 High resolution collimator 32 iterations High sensitivity collimator 200 iterations

30 Software applications: Investigating properties of reconstruction algorithms Simulating different hardware configurations and researching optimal scanning parameters, Education/Training in the field of nuclear medicine imaging.

31 Outline Single Photon Emission Tomography Why do we need more computational power? Our software Results and efficiency comparison

32 Software tested on: PC with Intel Core i7 950, 24GB RAM, GTX 480,

33 Total reconstruction time [min] Results 17 h 22,9min 0.34min 13,5 min Collimator For the one iteration we gain: 45 times faster reconstruction for matrix size 64 x 64 x times faster reconstruction for matrix size 128 x 128 x 128. (Gaussian rotator)

34 Time [s] Matrix size reconstruction time dependence for the 2.2 x HR collimator Matrix size [px] (bilinear rotator)

35 Matrix size reconstruction time dependence for the 2.2 x HR collimator (bilinear rotator)

36 Reconstruction time breakup (bilinear rotator) GPU CPU 10 iterations, high sensitivity collimator, image size: 128 3

37 Reconstruction time breakup (Gaussian rotator) GPU CPU 10 iterations, high sensitivity collimator, image size: 128 3

38 Conclusions GPU implementation reduces the computation time of the statistical image reconstruction in SPECT by a factor of about ~80 for typical image sizes. The speed-up factor grows with the size of image size; it may approach 200 for large images. For GPU implementation reducing the dimensions of image matrix may not be an effective way of decreasing the reconstruction time. Similarly, using non pixel based image representations, e.g. blobs, may be suboptimal to just applying a finer pixel grid. For standard SPECT seems to be the optimal image size, readily suitable to apply the fast FFT based filtering. Even higher speed gains could be obtained in CT, where typical image sizes are of the order of

39 thank you Jakub Pietrzak

40 Backup

41

42 Why Statistical Iterative Reconstruction? CT: FBP ASIR Low dose CT 120 kvp; 3.75-mm slice thickness Adaptive Statistical Iterative Reconstruction Technique for Radiation Dose Reduction in Chest CT: A Pilot Study. Singh S, Kalra, MK Radiology May 1, :

43 Why Statistical Iterative Reconstruction? The application of iterative reconstruction methods in computer tomography (CT) allows to reduce radiation dose by 60% with the same image quality. 150mAs FBP 40mAs ASIR Abdominal CT: Comparison of Low-Dose CT With Adaptive Statistical Iterative Reconstruction and Routine-Dose CT With Filtered Back Projection in 53 Patients Am. J. Roentgenol. September 1, :

44 25 mgy 12 mgy

45 X-ray computed tomography (CT)

46 Maximum likelihood expectation maximization g f M