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Ähnlich wie SPIE 10059-36(Reheman Baikejiang)
Ähnlich wie SPIE 10059-36(Reheman Baikejiang) (20)
SPIE 10059-36(Reheman Baikejiang)
- 1. Gaussian kernel based anatomically- aided diffuse optical tomography reconstruction Reheman Baikejiang, Wei Zhang, and Changqing Li SPIE 10059-36, January 31, 2017
- 2. 2/26 Outline • Background of DOT • Introduction of kernel method • Simulation Results • Phantom experiment result • Conclusions and future work
- 3. 3/26 Background of DOT DOT: also known as near-infrared (NIR) tomography, refers to the optical imaging of biological tissue in the diffusive regime. Photo courtesy of NIRx
- 4. 4/26 Background of DOT • Advantages – Safe, noninvasive and non-ionizing radiation – Intrinsic molecular sensitivity – Functional imaging – Low cost • Disadvantages – Low spatial resolution – Very sensitive to noise
- 5. 5/26 Anatomical guidance by Soft- prior Objective function with priori information: Soft-prior matrix:1 𝐿𝑖𝑗 = 0 if 𝑖 and 𝑗 are not in the same region −1/𝑁 if 𝑖 and 𝑗 are in the same region 1 if 𝑖 = 𝑗 [1] Phaneendra K. Yalavarthy et al., Opt. Express 15(13), 8176-8190 (2007)). (1) (2) Ω = min 𝜇 𝑎 {||𝑦 − 𝐹(𝜇 𝑎)||2 2 + 𝜆||𝐿(𝜇 𝑎 − 𝜇 𝑎0)||2 2 }
- 6. 6/26 Anatomical guidance by Soft- prior • Advantages Soft-prior method: – Easy to implement when segmented prior information available – Fast convergence • Why we introduce the kernel method: – Reduce the image segmentation process – Looking for new method which is robust to the incorrect prior information
- 7. 7/26 Outline • Background of DOT • Introduction of kernel method • Simulation and experimental setup • Results • Conclusions and future work
- 8. 8/26 Kernel method The absorption coefficient at a node 𝑖 can be written as: 𝜇 𝑎 𝑖 = 𝑗 𝛼𝑗 𝜅(𝒇𝑖, 𝒇 𝑗) Here we use Gaussian kernel: 𝜅 𝒇𝑖, 𝒇𝒋 = exp( − 𝒇 𝒊−𝒇 𝑗 2 𝜎2 ) In a matrix-vector form: 𝜇 𝑎 = 𝐾𝜶 (3) (4) (5)
- 9. 9/26 Kernel method Only the k-nearest neighbors(𝑘𝑛𝑛) are stored in the kernel matrix:2 𝐾𝑖𝑗 = 𝜅 𝒇𝑖, 𝒇 𝑗 , 𝒇𝒋 ∈ 𝑘𝑛𝑛 of 𝒇𝑖 0, otherwise Kernelized objective function is obtained as: Ω 𝜶 = 1 2 𝑦 − 𝐹 𝐾𝜶 2 2 Update equation: 𝐾 𝑇 𝐽 𝑇 𝐽𝐾 + 𝜆𝐼 Δ𝛼 𝑛 = 𝐾 𝑇 𝐽 𝑇 𝛿 𝑛−1 where 𝛿 is the data-model misfit, 𝛿 = 𝑦 − 𝐹(𝐾𝜶) Once 𝜶 is found, we can obtain 𝜇 𝑎 = 𝐾𝜶 (6) (7) (8) [2] Guobao Wang et al., IEEE Trans. Med. Imag.. (34)1 61-69 (2015).
- 10. 10/26 Outline • Background of DOT • Introduction of kernel method • Simulation Results • Phantom experiment result • Conclusions and future work
- 11. 11/26 Numerical simulation setup Diameter Height 𝝁 𝒂 𝝁 𝒔 ′ Background 78.0 mm 60.0 mm 0.007 mm-1 1.0 mm-1 Target 10.0 mm 10.0 mm 0.028 mm-1 1.0 mm-1 Optical properties and geometry dimensions of the phantom for the numerical simulation. Simulation Phantom geometry Source-detector nodes in one projection A cross section of simulated CT image
- 12. 12/26 Image quality evaluation metrics • VR = 𝑟𝑅𝑂𝐼 𝑅𝑂𝐼 Dice = 2∗ 𝑟𝑅𝑂𝐼∩ 𝑅𝑂𝐼 𝑟𝑅𝑂𝐼 + 𝑅𝑂𝐼 • CNR = 𝑀𝑒𝑎𝑛 𝑥 𝑅𝑂𝐼 −𝑀𝑒𝑎𝑛(𝑥 𝑅𝑂𝐵) 𝜔 𝑅𝑂𝐼 𝑉𝑎𝑟 𝑥 𝑅𝑂𝐼 + 1−𝜔 𝑅𝑂𝐼 𝑉𝑎𝑟(𝑥 𝑅𝑂𝐵) • MSE = 1 𝑁 𝑗=1 𝑁 𝑥𝑗 − 𝑥0 𝑗 2 Here: 𝜔 𝑅𝑂𝐼 = |𝑅𝑂𝐼|/( 𝑅𝑂𝐼 + 𝑅𝑂𝐵 ) ROI: region of interest , ROB: region of background
- 13. 13/26 Numerical Simulation Results (I) Grand truth No prior Soft prior k = 16, 3×3×3 k = 32, 3×3×3 k = 64, 3×3×3 k = 64, 5×5×5 k = 64, 7×7×7 k = 64, 9×9×9 Kernel Method
- 14. 14/26 Image quality evaluation metrics Voxel number VR Dice CNR 𝐌𝐒𝐄 Soft prior 1.0 1.0 138.57 2.47e-07 No prior 1.67 0 2.54 1.39e-07 The calculated VR, Dice, CNR and MSE with the kernel method for k = 16,32,64 k Voxel number VR Dice CNR 𝐌𝐒𝐄 16 3×3×3 0.52 0.69 16.49 8.55e-07 32 3×3×3 0.52 0.69 23.56 6.34e-07 64 3×3×3 0.52 0.69 22.16 4.40e-07 k Voxel number VR Dice CNR 𝐌𝐒𝐄 64 5×5×5 0.52 0.69 22.52 4.12e-07 64 7×7×7 0.52 0.69 22.51 3.93e-07 64 9×9×9 0.57 0.72 25.48 3.83e-07 The calculated VR, Dice, CNR and MSE with the kernel method for k = 64 and different voxel number The calculated VR, Dice, CNR and MSE with soft prior method and no prior.
- 15. 15/26 Numerical Simulation Results(II): Cancer contrast in CT image Tumor Glandular Adipose Skin Mean intensities of breast compositions in real CT image with iodine contrast injection One slice of CT image with iodine contrast injection
- 16. 16/26 Reconstructed DOT images with kernel method: CT contrast effect CT contrast VR Dice CNR 𝐌𝐒𝐄 1:2 0.52 0.69 26.65 3.97e-07 1:3 0.52 0.69 22.98 4.37e-07 1:6 0.57 0.72 28.57 3.47e-07 The calculated VR, Dice, CNR and MSE for the reconstructed absorption coefficient images with different background to target CT contrasts. With CT contrast 1:2 With CT contrast 1:2 With CT contrast 1:6
- 17. 17/26 Numerical Simulation Results(III): False positive target effect Grand truth (𝜇 𝑎)simulated CT image Kernel method (k=64,9×9×9 ) Soft prior
- 18. 18/26 Numerical Simulation: clinical CT image as guidance Breast CT image with iodine contrast injection, used in kernel method (without segmentation) Segmented breast shape and tumor region, used in soft prior method
- 19. 19/26 Numerical Simulation Results(IV): Source-detector and mesh Finite element mesh of breast shape generated form CT image Source-detector nodes in one projection
- 20. 20/26 Numerical Simulation: Reconstructed DOT image Reconstructed DOT image by soft prior method Reconstructed DOT image by kernel method with k=64 and voxel numbers of 9×9×9
- 21. 21/26 Outline • Background of DOT • Introduction of kernel method • Simulation Results • Phantom experiment result • Conclusions and future work
- 22. 22/26 DOT prototype system Prototype DOT system
- 23. 23/26 Phantom experimental setup and CT image Diameter Height 𝝁 𝒂 𝝁 𝒔 ′ Background 78.0 mm 60.0 mm 0.007 mm-1 1.0 mm-1 Target 10.86 mm 13.63 mm 0.028 mm-1 1.0 mm-1 Optical properties and geometry dimensions of the experimental phantom. Phantom geometry. Slice of CT image Target region filled
- 24. 24/26 Phantom experimental results VR Dice CNR No prior 0.88 0.0 0.48 Soft prior 1.0 1.0 246.20 Kernel method 0.65 0.76 16.03 Image quality metrics of reconstructed DOT image without the structural guidance with soft prior method With kernel method (k=64, voxel number 9×9×9)
- 25. 25/26 Summary and Future Work • Summary: • We propose the kernel method to introduce the anatomical guidance into the DOT image reconstruction. Compared with the conventional structural prior guided DOT reconstruction algorithms, such as soft- prior, the proposed method has the advantage of not requiring the image segmentation and region classification. Robust to a false positive target prior. • Future Work: • Investigating proposed method with a clinical data
- 26. 26/26 Acknowledgement • Authors thank research support from : • California Breast Cancer Research Program (IDEA: 20IB-0125) • Startup fund from UC Merced • Travel award from the graduate program of Biological Engineering and Small Technologies, UC Merced. • Authors also thank : • Professor John M. Boone, in Department of Radiology, UC Davis for the phantom CT scan and clinical breast CT data • Professor Ramsey D. Badawi, in Department of Radiology, UC Davis for helpful discussions.
- 27. Thank you for your attention! Any Questions?
Hinweis der Redaktion
- Diffuse optical tomography, also known as near-infrared (NIR) tomography, refers to the optical imaging of biological tissue in the scattering medium. Photons in turbid medium scatters like the picture on the right which makes hard reconstructing the absorbing structure from the limited number of measurements.
- The advantages of DOT are: it is safe, noninvasive and non-ionizing radiation. It is functional imaging modelity which has high molecular sensitivity. Furthermore, it is cost efficient. However, it has some disadvantages: such as, low spatial resolution and very sensitive to noise.
- To improve the spatial resolution DOT, anatomical images are introduced to guide DOT reconstruction. Among the many methods, Soft prior method have proven to be most effective and widely applied in structural guided DOT image reconstruction. In which, soft prior matrix L is obtained from segmented anatomical images, then incorporated into the regularization term of the objective function. In continuous wave(CW) domain, objective function of DOT is given by equation (1). Here Mua is absorption coefficient, F is forward operator which can be solved by Finite element method. Each element of regularization matrix L is obtained by the equation 2. Here N is the number of finite element mesh nodes comprising a given region.
- For the next few slides, I will introduce the implementation of kernel method in DOT reconstruction.
- Here we adopted the kernel method from the position emission tomography. In this method, we can write unknown absorption coefficient at the mesh node j as a combination of kernel functions described in equation (3). Here are alpha is kernel coefficient, which is also intermediate unknown to be found. fi and fj are feature vectors extracted from anatomical images. The picture on the right depicts how the feature vectors extracted from the anatomical images in 2D. But in our study, we used 3D image. The size of feature vectors differs depending on the voxel numbers we consider for each mesh node. Sigma is a free parameter. In this study, we used Sigma as 1, which is proved to be best in our another study.
- For the sake of computational efficiency, we only considered k-nearest neighbors in the kernel matrix, which can be found by Matlab built-in function (knnsearch). The kernelized objective function can be written as equation (7), By newton’s method, the update equation at the iteration n can be written as equation (8), where 𝛿 is the data-model misfit. Once we find the alpha, we can obtain asorption coeffienct by the equation (5)
- In the next few slides, I will show our numerical simulation results.
- In the numerical simulations, we used a cylindrical phantom with a diameter of 78 mm and a height of 60 mm. A cylindrical target (diameter of 10 mm and height of 10 mm) was placed at 15 mm away from the center line of the phantom and 20 mm below of the top surface of the phantom in the vertical direction as shown in figure left most. Numerical DOT measurement data at six angular projections were generated by the DOT forward model. In each angular projection, six source positions were placed on one side of the phantom in the vertical line as indicated by the black dots in Figure. Six source positions were separated 5 mm apart. A rectangular region on the opposite side of the numerical phantom was chosen to be the field of view (FOV) and all surface nodes within this region were used as measurement detectors as indicated by the red dots in Fig. 1(b). Then, we added 15% Gaussian noise (signal to noise ratio (SNR) of 27.24 dB) to the numerical DOT measurement data. Corresponding 3D CT image also generated with CT contrast approximately 1:5.
- The Volume Ratio (VR) measures the ratio between the true region of interest (ROI) and the reconstructed region of interest (rROI), where |.| denotes the number of elements of the set, and the rROI contains the reconstructed signals with amplitudes higher than half of the maximum amplitude of all reconstructed signals. Ideally, VR should be close to 1. The dice similarity coefficient (Dice) measures the location accuracy of the reconstructed target with respect to the true location. In the ideal case, Dice should also be close to 1. The Contrast-to-Noise Ratio (CNR) measures how easy it is to see the reconstructed target from the background, region and f denotes the reconstructed signal. A high CNR value means a high contrast between the reconstructed target and the background, which is preferred. The Mean Square Error (MSE) measures the difference between the approximation and the truth, where x0 is the true signal.
- The ground truth absorption coefficient distribution image shown at top left most. Next to it is reconstruction DOT image without any structural information. Top right is reconstruction result with soft prior method. Bottom two row is reconstructed DOT images with proposed kernel method. From those figures, we can see the quality of reconstruction results are improving when voxel number in feature vector and k value in k-nearest neighbor are increase.
- which indicates that the reconstruction with the soft prior method is the best with both VR and Dice coefficients of 1 and the lowest MSE. We also see that the DOT reconstruction without any structural guidance is the worst with VR much greater than 1 and Dice coefficient of 0. For the cases with the kernel method, MSE decreases nearly linearly when k and voxel number increase. Reconstructed DOT image for k=64 and voxel number of 9×9×9 is the best among all the cases of the kernel method with the highest CNR of 25.48 and the lowest MSE of 3.83e-07. VR and Dice coefficients are the same for all the combinations of the kernel method, except for the case k=64 and voxel number of 9×9×9 with the highest VR of 0.57 and Dice of 0.72.
- This is a sample CT image for breast cancer patient iodine contrast agent injected. As we know , there is early stage tumor in the middle of the image . Bottom table shows mean intensity of different compositions of the breast. The next question we want answers is how the background and target contrast in anatomical image will effect the reconstruction result of proposed method.
- The geometry and optical properties are all same with previous simulation. We only changed the background to target CT contrast. From the reconstructed DOT images and quality evaluation metrics, we can see that there is no significant change in the reconstruction result.
- In this simulation, we intendedly embedded another target in the prior CT image, which is not exist in the DOT simulation setup. The bottom left figure is the result with soft prior method. In which false target is also observed. On the right, reconstruction result with Kernel method. Although there are some artifacts around boundary, we can’t see false positive target on the bottom.
- In this simulation we used clinical CT image with iodine contrast injected patient. We segmented breast shape and tumor to generate DOT measurement. For reconstruction, we use real CT image in Kernel method. And generated soft prior matrix from the segmented image.
- Numerical simulating setup almost similar to our previous simulation. Six projection with six source position using transmission mode. Figure on right is FE mesh generated from the CT image.
- The figure on the left is reconstruction result with soft prior method. The figure on right is reconstructed DOT image by kernel method with k=64 and voxel numbers of 9×9×9. This simulation indicates , the proposed method is feasible with breast CT data.
- Next, we validated proposed method with phantom experiment.
- Phantom geometry is almost similar to our numerical phantom simulation. Phantom was made of 2% Agar, Titanium dioxide (TiO2) as scattering particles, Indian ink as absorber. Since optical absorption contrast alone does have CT contrast, The target is embedded inside transparent glass tube. only the glass tube was observed in the reconstructed CT images, we filled the target regions by pixels having the same CT contrast as the glass tube to provide anatomical guidance in the kernel method.
- The kernel method reconstruction has the coparable results with the soft prior method in terms of the image evaluation metrics .