Fully3D Advanced System Models for Reconstruction in Flat-Panel Detector Cone-Beam CT Steven Tilley, Jeffrey Siewerdsen, Web Stayman Johns Hopkins University Schools of Medicine and Engineering Acknowledgements AIAI Laboratory Advanced Imaging Algorithms and Instrumentation Lab aiai.jhu.edu web.stayman@jhu.edu I-STAR Laboratory Imaging for Surgery, Therapy, and Radiology istar.jhu.edu jeff.siewerdsen@jhu.edu Faculty and Scientists Tharindu De Silva Grace Gang Aswin Mathews Amir Pourmorteza Jeffrey Siewerdsen Alejandro Sisniega Shiyu Xu Wojciech Zbijewski Students Qian Cao Hao Dang Sarah Ouadah Sureerat Reaungamornrat Steven Tilley II Ali Uneri Jennifer Xu Thomas Yi Industry Partners Sungwon Yoon Kevin Holt David Nisius Edward Shapiro Funding Supported in part by a Varian industry partnership and NIH grants R21-EB-014964 and T32-EB010021 This work was supported, in part, by the above grants. The contents of this presentation are solely the responsibility of the authors and do not necessarily represent the official view of Johns Hopkins or the NIH. Johns Hopkins University 1
Noise model and reality mismatch Normalized Detector Units Normalized Detector Units Source and Detector Blur Modeling Mean: g y 0 = B s D g exp( Aμ) y = B d B s D g exp( Aμ) Source Blur B s Extended X-ray Source B s Light Photons B d Detector Blur B d X-ray Photons Photodiodes Object Scintillator Covariance: D{g} D{ y 0 } B d D y 0 B d T B d D y 0 B d T + K ro Quanta: Uncorrelated Bare Beam Uncorrelated, Attenuated X-rays with Focal Spot Blur Correlated Light Photons with Light Spread Correlated Electrons with Readout Noise Forward Model: Noise Model: y(μ) = B d B s D g exp( Aμ) y~gaussian( y, K y ) K Y = B d D y 0 B d T + K ro Johns Hopkins University 2
Simple estimate from forward model: l = log D 1 g B 1 y B = B d B s Linearization Estimated Covariance of l 1 K L D B 1 y B 1 K Y B 1 T D 1 B 1 y Blurs may have nullspaces/regions of poor invertiblilty. B 1 C 1 = masked deblur C C 1 1 = masked blur K 1 L D C 1 y C B d D C 1 y B T d + K2 σro 1 C T D C 1 y Objective Function Φ μ = ψ μ L = l) + βp(μ) Likelihood Term Penalty Term Where l is an estimate of the line integrals and µ is the attenuation values If the line integrals are from a Gaussian distribution: ψ μ L = l) = Aμ l KL = Aμ l T K L 1 Aμ l : weighted least squares If P μ = μ T Rμ (quadratic) then: μ = A T K L 1 A βr 1 A T K L 1 l Johns Hopkins University 3
Solving Strategy μ = A T K L 1 A βr 1 A T K L 1 l Preprocessing: l = [ log D 1 g C 1 y ] b = A T K 1 L l Solve using CG A T K 1 L A + βr μ = b Evalulate K L 1 x: p = C T D C 1 y x solve for q using CG where: K Y q = p b = D C 1 y C q return b K L 1 D C 1 y C T K Y 1 C D C 1 y Simulation Phantom Metrics: Resolution edge response of disk Variance spatial variance center of disk in Comparisons are made to an uncorrelated noise model: 1 K L = C 1 2 y + σ ro Phantom: 4000x4000 25x25 µm voxels projected onto 7000 35x35 µm pixels Reconstruction: 1000x1000 100x100 µm voxels with 1750 140x140 µm pixels Geometry: SAD = 600, SDD = 1200, 720 angles, full rotation Johns Hopkins University 4
Simulation Phantom Reconstructions Varying Blur Distribution 2 FWHM Total = FWHM s 2 + FWHM d 2 = Constant Assess effects of varying different types of blur when total blur is constant Johns Hopkins University 5
Varying Total Blur FWHM s FWHM d = Constant Assess effects of varying total blur when the ratio of blur widths is constant Test Bench Studies Volume: 210x600x600 Voxels: 150 µm 720 Projections Full orbit SDD: 1180 mm SAD: 600 mm Pixels: 388x388 µm 100 kvp 0.63 mas per projection Johns Hopkins University 6
Detector MTF Measurements E. Samei, M. J. Flynn, and D. a. Reimann, A method for measuring the presampled MTF of digital radiographic systems using an edge test device, Med. Phys., vol. 25, no. 1, p. 102, 1998. Source MTF Johns Hopkins University 7
Bench Data Reconstruction Bench Data Reconstruction Difference from high resolution reference Johns Hopkins University 8
Conclusion - More accurate noise models improve model based algorithms. - Modeling noise correlations are important in the presence of large source blurs. - Clinical systems with specs similar to our test bench will be able to better resolve fine structure such as trabeculae using this method Future directions - Model higher order characteristics of source blur - Nonlinear objective function Source Pinhole image Johns Hopkins University 9