F3-A5: Toward Model-Based Reconstruction in Scanned Baggage Security Applications

Transcription

1 F3-A5: Toward Model-Based Reconstruction in Scanned Baggage Security Applications Abstract While traditional direct reconstruction algorithms such as filtered back projection depend on the analytic inversion of sinogram data, model-based reconstruction methods are based on the iterative optimization of a statistical model of both the acquired data and the unknown image. Model-based reconstruction offers many important potential advantages over traditional methods of direct reconstruction for the security screening of checked baggage. It has the potential to reduce metal artifacts, improve resolution, reduce artifacts such as cupping that can systematically distort CT number estimates, incorporate tighter integration of reconstruction and segmentation, and support reconstruction from scanners with a small number of projections. All these enhancements have the potential to improve the P d /P fa tradeoff for CT security screening systems. The objective of this research is to investigate and quantify the value of model-based reconstruction for baggage security screening. To do this, our first goal is to implement a general model-based reconstruction algorithm for use on multi-slice helical scan CT scanners and to test and evaluate this algorithm on scans of luggage provided by the ALERT Center. In addition, we will have an ongoing goal of identifying and investigating opportunities for adapting and improving the model-based reconstruction technology for use in security applications. In particular, we will study the use of advanced forward and prior models for reducing metal artifacts, improving segmentation accuracy, and improving CT number estimation. I. PARTICIPANTS Faculty/Staff Name Title Institution Phone Charles A. Bouman Professor Purdue University bouman@ecn.purdue.edu Ken D. Sauer Professor Notre Dame University sauer@nd.edu Students Name Degree Pursued Institution Intended Year of Graduation Pengchong Jin Ph. D. Purdue University Jin36@purdue.edu 2013 Eri Haneda Postdoc Purdue University Haneda@purdue.edu 2011 II. PROJECT OVERVIEW AND SIGNIFICANCE While traditional direct reconstruction algorithms such as filtered back projection depend on the analytic inversion of sinogram data, model-based reconstruction methods are based on iterative optimization of a statistical model of both the acquired data and the unknown image. This structure means that model-based reconstruction algorithms can incorporate both specific details of geometry or physics for the scanner and a statistical characterization of the objects reconstruction. Advances in algorithms, models, and computation over recent years have allowed the methods of model-based reconstruction to be practically applied to the problem of medical image reconstruction for multi-slice helical scan CT [1,2,3,4,5]. The results of these studies support the idea that model-based reconstruction can improve image quality and dramatically reduce

2 dosage for medical applications. However, the problems faced in applications of CT to security image scanning are quite different than those for medical applications, so questions remain as to the potential advantages of model-based reconstruction in security applications. In the security scanning application, dosage reduction is not as important as it is in the medical case. However, model-based reconstruction holds potential to improve performance of EDS equipment through increased probability of detection (Pd), decreased probability of false alarm (Pfa), increasing the population of detected objects including additional HMEs, and reducing the mass per object required for detection. More specifically, model-based reconstruction has the potential to achieve these long-term goals through: Reduced metal artifacts Streaks resulting from metal artifacts can adversely affect segmentation algorithms, thereby degrading the Pd/Pfa tradeoff [6,7]. Reduced noise Effects such as photon starvation, which degrade image quality, can be substantially reduced with model-based reconstruction [8]. Increased resolution Improved resolution can better separate materials and detect smaller masses. Reduced beam hardening and scatter artifacts Model-based reconstruction can be used to better model beam-hardening and scatter artifacts, thereby reducing cupping artifacts, and achieving more accurate estimates of CT number. Dual energy Model-based dual energy reconstruction can achieve more accurate estimates of CT number and Z eff by explicitly modeling beam hardening effects. Integrated reconstruction/segmentation Model-based reconstruction allows for the direct integration of segmentation information into the prior model, which can potentially enhance the accuracy of CT number estimation [9, 10]. Reconstruction from limited view data Model-based reconstruction offers the possibility of computing accurate reconstructions from finite view data (< 20 views), which in turn offers new alternatives in the concept of operation. [11] The objective of this research is to investigate and quantify the value of model-based reconstruction for baggage security screening and to develop novel methods for the improvement of model-based reconstruction in its application to CT security scanning of baggage. To this end, we will have two project-period goals, with the first goal being the implementation and assessment of a state-of-the-art model-based reconstruction algorithm for use on multi-slice helical scan CT data, and the second goal being the identification and development of novel forward and prior modeling approaches for the enhancement of image quality in security scanning applications. All research performed for this project will depend on the development of completely new C and C++ software since existing code is proprietary. In order to achieve our first goal, we will implement a state-of-the-art model-based reconstruction method for use on multi-slice helical scan CT, which will include the steps of a) implementation of a general purpose helical-scan multi-slice CT forward projector based on a distance-driven forward projector [5,4]; b) implementation of a maximum a posteriori (MAP) reconstruction algorithm based on the use of iterative coordinate descent (ICD) optimization [1,2]; c) implementation of a CT acquisition noise model-based on a photon-counting model with additive Gaussian electronic noise; d) implementation of a Markov random field prior model using the q-ggmrf (Generalized Gaussian Markov Random Field) prior with the surrogate function optimization techniques [3,4]; e) parallelization of the code for use on a shared memory multi-core architecture using p-thread parallelization; f) implementation of the non-homogeneous ICD optimization technique for fast convergence of the reconstruction [5]. Once fully implemented, we will use a combination of synthetically generated data together with the true CT scanner data provided by ALERT to test and evaluate our algorithms and to access image quality. With these results, we will also access potential directions for improvements of the algorithms.

3 III. RESEARCH AND EDUCATION ACTIVITY A. State-of-the-Art and Technical Approach Figure 1 a) and b) below illustrate the comparison between state-of-the-art filtered-back projection and the model-based iterative reconstruction (MBIR) method implemented on a 64 slice GE scanner. Notice the substantial noise reduction, improved resolution and reduced artifacts of the MBIR reconstruction as described in [4]. Below we give a more detailed mathematical description of the model-based reconstruction method we have implemented. MAP Reconstruction Model-based reconstruction works by incorporating a model of both the tomographic scanner and the image being reconstructed. A typical approach is to compute the maximum a posteriori (MAP) estimate given by: Figure 1a: FBP and MBIR reconstructions using GE Veo system of routine abdomen pelvis Dose 0.77 msv kvp ma. where p(y x) is the conditional distribution of projection data vector y given true image x, p(x) is the prior distribution of x, and x>0 indicates that each voxel must be non-negative. In this study, we use a Taylor series expansion to approximate the log likelihood term using a quadratic function, resulting in: Figure 1b: FBP and MBIR reconstructions using GE Veo system of routine head Dose 0.5 msv 120 kvp ma. where A i,* = ith row of A, y i =, A is the forward system matrix, λ i is the i th detector measurement, λ o,1 is the i th detector air-calibration measurement, and D is a diagonal weighting matrix. For the computation of the forward projection matrix, we used the distance driven forward model described in [5,4]. The log prior term controls the smoothness of the reconstructed image, and its selection is the key to minimizing artifacts and enhancing resolution, particularly when the scanning geometry limits special sampling. In this approach, we use the q-ggmrf model of [5,6], which is a generalization of the GGMRF of [3]. Our prior model has the form where ρ(δ) has the form specified by the q-ggmrf prior given by 1 Dose calc: Anatomy = 1/2 Pelvis, 1/2 Abdomen = DLP (45*.5*.019) + (45*.5*.015) = = 0.77

4 ICD Algorithm Our initial implementation uses the ICD for minimization of the MAP cost function [1,2,6]. The ICD algorithms has the form: where s is the set of neighboring voxels to s 1, and Θ 1 and Θ 2 are the first and second derivatives of the likelihood function with respect to the voxel x s. In order to solve the 1-D optimization problem, we use the methods of surrogate functions [7]. Forward Projector Multi-slice helical CT has a cone-beam structure where a gantry (X-ray source and detector array) rotates around an object in a helical scan path as shown in Figure 2. The detector array typically consists of hundreds of channels and several rows. In the applications such as checked-baggage inspection, the object often contains high-density materials such as metal. This results in low signal-to-noise ratio measurement due to the high attenuation of the material. This unreliable measurement is typically visible as a streak artifact in the reconstruction. Figure 2: Graphic illustration of the geometry for a multi-slice helical scan CT system. Collected data is indexed by view angle, detector column, and detector row. Figures on right illustrate the projection geometry used to compute B_i,j and C_i,j, where A_i,j = B_i,j x C_i,j. Multi-Core Parallelization In order to reduce reconstruction time, we have parallelized the algorithm using p-threads on a multicore shared memory architecture. Figure 3 illustrates how each core was assigned a range of image slices. Then a single core updates one z-line at a time by updating the voxels in sequence along the z coordinate. This method has much better cache efficiency. Non-homogeneous ICD Algorithm In order to further speed convergence, we also use the non-homogeneous ICD method [7]. The idea is to focus computation on voxels, which tend to generate significant updates. In NH-ICD, we alternate between a full scan and a partial scan which involves only those voxels, which have significant updates at the previous iteration. V map is basically a 2D map and V(jx,jy) records the total update values of voxels at (jx, jy) after a full homogeneous scan. Figure 4 illustrates the flowchart of NH-ICD algorithm.

5 Reconstruction Results Figure 3: Illustration of our cores are allocated to different groups of pixels. Each core updates voxels along a z-line in sequence in order to maximize cache efficiency. Plot shows speedup as a function of the number of cores utilized. Figure 5 shows the quality of different reconstruction algorithms. The projection data is provided by ALERT and is produced with pitch 1 (i.e. 16 detectors per rotation) on a 16-slice scanner with voxels of dimension 0.975mm x 0.975mm x 1.25mm. The FBP reconstructions are provided by ALERT. They are blurred. Some objects in FBP reconstructions are distorted. And the severe streaking artifacts around the high objects can also be observed. On the other hand, our model-based algorithm offers better reconstructions. The images are sharper and shapes of objects are more accurately recovered. In addition, the streaking artifacts are greatly reduced. Novel Prior Modeling Recent research in image denoising indicates that dictionary-based learning techniques can be used to substantially improve results as compared to classical MAP inverse methods. We developed a novel prior modeling method based on implicit Gibbs distribution can be used in MAP tomographic reconstruction to substantially improve reconstructed image quality. Our approach is to approximate the true prior using a surrogate energy function with the form: Figure 4 (left): flowchart of NH-ICD algorithm. Figure 5 (right): Images (a, c) are the FBP reconstructions provided by ALERT. Images (b, d) are the model-based reconstructions generated by our algorithm. All images are displayed with window [0, 1600] HU.

6 where coefficients of B and d can be calculated by training the local image patches. Then we iteratively minimize the substitute functional to get the converged reconstruction results. The algorithm is as follows: The model of the local image patches is free to choose and currently we used the Gaussian mixture model (GMM). Figure 6 shows some of our preliminary simulated results using implicit prior model. The simulated data is a 128 x 128 parallel beam phantom with 1mm pixel width. We had 90 views and 2 degree per view. Figure 6: reconstruction results using different priors on simulated data. (a) is the original phantom. (b) is the FBP reconstruction. (c) is the reconstruction using q-ggmrf prior and (d) is the reconstruction using implicit prior method. All images are displayed with window [0, 1600] HU.

7 B. Major Contributions We have designed and implemented a model-based reconstruction algorithm for multi-slice helical scan data, and we have parallelized the algorithm for a multicore shared memory architecture using p-threads. We have demonstrated the operation of these algorthms on both the simulated data and the real data. We have showed the potential advantages of our model-based algorithm over the traditional FBP approach. In addition, a novel prior modeling techniques is also developed and has been applied to the simulated data and it generated very promising results. IV. FUTURE PLANS In the near term, we will continue to refine our algorithm to produce qualitatively higher quality images. To do this, we will adjust geometry of our model to better fit the physical data, and we will optimize the parameters of the prior and forward models to optimize image quality. Also, we plan to compare our algorithm with other analytical algorithms, such as Advanced Single Slice Rebinning (ASSR). Once this task is complete, we will indentify the most important aspects of image degredation, such as metal artifacts or systematic errors in CT number estimates resulting from artifacts, and we will formated improve forward and prior models to enhance reconstructed image quality and ultimately improve the the Pd/Pfa tradeoff. Also, we will refine our implicit prior model and try to apply this method to the real data provided by ALERT and assess its applicability in security application. V. DOCUMENTATION A. Publications 1. P. Jin, E. Haneda, C. Bouman and K. Sauer, A Model-based 3D Multi-slice Helical CT Reconstruction Algorithm for Transportation Security Application, the 2nd International Conference on Image Formation in X-ray Computed Tomography, June, E. Haneda, C. Bouman, Implicit priors for model based inversion, IEEE International Conference on Acoustics, Speech, and Signal Processing, March, S. J. Kisner, E. Haneda, C. Bouman, S. Skatter, M. Kourinny and S. Bedford, Limited view angle iterative CT reconstruction, in Proc. SPIE, vol. 8296, 2012, p F. 4. S. J. Kisner, E. Haneda, C. Bouman, S. Skatter, M. Kourinny and S. Bedford, Model-based CT Reconstruction from Sparse Views the 2nd International Conference on Image Formation in X-ray Computed Tomography, June, B. Technology Transfer None to date. C. Seminars, Workshops, and Short Courses At Electronic Imaging Symposium as part of the Computational Imaging Conference IIX SPIE Vol on Tuesday January 25, 2011, Dr. Samit Basu of Safran Morpho Detection and Prof. Charles Bouman organized a special session entitled Advance Methods in Tomographic Imaging, which brought together leading researchers in CT algorithms and hardware from around the world, with a particular focus on CT applications in security imaging. (See: page 42 )

8 VI. REFERENCES [1] K. Sauer and C. Bouman, A local update strategy for iterative reconstruction from projections, IEEE Trans. On Signal Processing, vol. 41, no 2, 1993 [2] C. A. Bouman and K. Sauer, A Unified Approach to Statistical Tomography using Coordinate Descent Optimization, IEEE Trans. on Image Processing, vol. 5, no. 3, pp , March [3] C. Bouman and K. Sauer, A Generalized Gaussian Image Model for Edge-Preserving MAP Estimation, IEEE Trans. on Image Processing, vol. 2, no. 3, pp , July [4] J. B. Thibault, K. D. Sauer, C. A. Bouman, and J. Hsieh, A Three-Dimensional Statistical Approach to Improved Image Quality for Multi-Slice Helical CT, Med. Phys., vol. 34, no. 11, pp , [5] Synho Do, Zhuangli Liang, William Clem Karl, Thomas Brady, and Homer Pien, A Projection Driven Precorrection Technique for Iterative Reconstruction of Helical Cone-Beam Cardiac CT Images, Proceedings of SPIE Medical Imaging 2008: Physics of Medical Imaging, Jiang Hsieh and Ehsan Samei, Eds., 2008, vol [6] B. DeMan and S. Basu, Distance-Driven Projection and Backprojection in Three-Dimensions, Phys. Med. Biol. 49, pp , [7] Z. Yu, J.B. Thibault, C. A. Bouman, K. D. Sauer, and J. Hsieh, ``Fast Model-Based X-ray CT Reconstruction Using Spatially Non-Homogeneous ICD Optimization, IEEE Trans. on Image Processing, vol. 20, no. 1, pp , January [8] J.-B. Thibault, C. A. Bouman, K. D. Sauer, J. Hsieh, A Recursive Filter for Noise Reduction in Statistical Iterative Tomographic Imaging, SPIE/IS&T Conference on Computational Imaging IV, vol. 6065, San Jose CA, Jan , [9] K. Sauer, and C. Bouman, Bayesian Estimation of Transmission Tomograms Using Segmentation Based Optimization, IEEE Trans. on Nuclear Science, vol. 39, no. 4, pp , Aug [10] T. Frese, C. A. Bouman, and K. Sauer, Multiscale Bayesian Methods for Discrete Tomography, Discrete Tomography: Foundations, Algorithms and Applications, edited by Gabor T. Herman and Attila Kuba, pp , Birkhauser Boston, Cambridge, MA, [11] S. J. Kisner, E. Haneda, C. Bouman, S. Skatter, M. Kourinny and S. Bedford, Limited view angle iterative CT reconstruction, in Proc. SPIE, vol. 8296, 2012, p F.