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Title: Two-dimensional iterative region-of-interest (ROI) reconstruction from truncated projection data

Abstract

A small detector or limited gantry rotation angles may cause data truncation, in which case the entire object cannot be completely reconstructed. However, a small region of interest (ROI) may be recoverable in certain truncation situations. Two analytical methods have been proposed for exact ROI reconstruction. Here we evaluate the capability of ROI reconstruction using an maximum-likelihood expectation-maximization (ML-EM) method, which directly solves the inverse problem of the system equations. ROI reconstruction using the ML-EM method is compared with that using the two analytical methods. Comparisons are based on reconstructions of four specifically designed, computer-simulated truncation cases. In the simulation, each reconstructed ROI is coupled with its counterpart in the nontruncated case to evaluate the accuracy of the reconstructed ROI. We found that, (a) in two truncation situations the ROI can be reconstructed by both the analytical methods and the two-dimensional ML-EM method, but the ML-EM method may produce a larger ROI; (b) for a truncation case that neither analytical algorithm is applicable, the ML-EM method provides a quantitative ROI reconstruction; and (c) for the well-known 'interior' truncation problem, neither the analytical methods nor the ML-EM method can perform an exact ROI reconstruction, but the ML-EM method provides informative ROImore » images. We also propose an analysis using the truncated projection matrix and its Moore-Penrose inverse matrix which can help to determine the recoverable ROI using iterative methods for a given truncation situation.« less

Authors:
;  [1]
  1. Utah Center for Advanced Imaging Research, University of Utah, Salt Lake City, Utah 84108 (United States)
Publication Date:
OSTI Identifier:
20951106
Resource Type:
Journal Article
Resource Relation:
Journal Name: Medical Physics; Journal Volume: 34; Journal Issue: 3; Other Information: DOI: 10.1118/1.2436969; (c) 2007 American Association of Physicists in Medicine; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
62 RADIOLOGY AND NUCLEAR MEDICINE; ACCURACY; ALGORITHMS; COMPUTERIZED SIMULATION; IMAGE PROCESSING; IMAGES; ITERATIVE METHODS; MAXIMUM-LIKELIHOOD FIT; SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY

Citation Formats

Zhang, B., and Zeng, G. L.. Two-dimensional iterative region-of-interest (ROI) reconstruction from truncated projection data. United States: N. p., 2007. Web. doi:10.1118/1.2436969.
Zhang, B., & Zeng, G. L.. Two-dimensional iterative region-of-interest (ROI) reconstruction from truncated projection data. United States. doi:10.1118/1.2436969.
Zhang, B., and Zeng, G. L.. Thu . "Two-dimensional iterative region-of-interest (ROI) reconstruction from truncated projection data". United States. doi:10.1118/1.2436969.
@article{osti_20951106,
title = {Two-dimensional iterative region-of-interest (ROI) reconstruction from truncated projection data},
author = {Zhang, B. and Zeng, G. L.},
abstractNote = {A small detector or limited gantry rotation angles may cause data truncation, in which case the entire object cannot be completely reconstructed. However, a small region of interest (ROI) may be recoverable in certain truncation situations. Two analytical methods have been proposed for exact ROI reconstruction. Here we evaluate the capability of ROI reconstruction using an maximum-likelihood expectation-maximization (ML-EM) method, which directly solves the inverse problem of the system equations. ROI reconstruction using the ML-EM method is compared with that using the two analytical methods. Comparisons are based on reconstructions of four specifically designed, computer-simulated truncation cases. In the simulation, each reconstructed ROI is coupled with its counterpart in the nontruncated case to evaluate the accuracy of the reconstructed ROI. We found that, (a) in two truncation situations the ROI can be reconstructed by both the analytical methods and the two-dimensional ML-EM method, but the ML-EM method may produce a larger ROI; (b) for a truncation case that neither analytical algorithm is applicable, the ML-EM method provides a quantitative ROI reconstruction; and (c) for the well-known 'interior' truncation problem, neither the analytical methods nor the ML-EM method can perform an exact ROI reconstruction, but the ML-EM method provides informative ROI images. We also propose an analysis using the truncated projection matrix and its Moore-Penrose inverse matrix which can help to determine the recoverable ROI using iterative methods for a given truncation situation.},
doi = {10.1118/1.2436969},
journal = {Medical Physics},
number = 3,
volume = 34,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • Various methods have been proposed for tomographic reconstruction from truncated projection data. In this paper, a reconstructive method is discussed which consists of iterations of filtered back-projection, reprojection and some nonlinear processings. First, the method is so constructed that it converges to a fixed point. Then, to examine its effectiveness, comparisons are made by computer experiments with two existing reconstructive methods for truncated projection data, that is, the method of extrapolation based on the smooth assumption followed by filtered back-projection, and modified additive ART.
  • A rotating slat collimator can be used to acquire planar-integral data. It achieves higher geometric efficiency than a parallel-hole collimator by accepting more photons, but the planar-integral data contain less tomographic information that may result in larger noise amplification in the reconstruction. Lodge evaluated the rotating slat system and the parallel-hole system based on noise behavior for an FBP reconstruction. Here, we evaluate the noise propagation properties of the two collimation systems for iterative reconstruction. We extend Huesman's noise propagation analysis of the line-integral system to the planar-integral case, and show that approximately 2.0(D/dp) SPECT angles, 2.5(D/dp) self-spinning angles atmore » each detector position, and a 0.5dp detector sampling interval are required in order for the planar-integral data to be efficiently utilized. Here, D is the diameter of the object and dp is the linear dimension of the voxels that subdivide the object. The noise propagation behaviors of the two systems are then compared based on a least-square reconstruction using the ratio of the SNR in the image reconstructed using a planar-integral system to that reconstructed using a line-integral system. The ratio is found to be proportional to {radical}(F/D), where F is a geometric efficiency factor. This result has been verified by computer simulations. It confirms that for an iterative reconstruction, the noise tradeoff of the two systems is not only dependent on the increase of the geometric efficiency afforded by the planar projection method, but also dependent on the size of the object. The planar-integral system works better for small objects, while the line-integral system performs better for large ones. This result is consistent with Lodge's results based on the FBP method.« less
  • Purpose: To generalize and experimentally validate a novel algorithm for reconstructing the 3D pose (position and orientation) of implanted brachytherapy seeds from a set of a few measured 2D cone-beam CT (CBCT) x-ray projections. Methods: The iterative forward projection matching (IFPM) algorithm was generalized to reconstruct the 3D pose, as well as the centroid, of brachytherapy seeds from three to ten measured 2D projections. The gIFPM algorithm finds the set of seed poses that minimizes the sum-of-squared-difference of the pixel-by-pixel intensities between computed and measured autosegmented radiographic projections of the implant. Numerical simulations of clinically realistic brachytherapy seed configurations weremore » performed to demonstrate the proof of principle. An in-house machined brachytherapy phantom, which supports precise specification of seed position and orientation at known values for simulated implant geometries, was used to experimentally validate this algorithm. The phantom was scanned on an ACUITY CBCT digital simulator over a full 660 sinogram projections. Three to ten x-ray images were selected from the full set of CBCT sinogram projections and postprocessed to create binary seed-only images. Results: In the numerical simulations, seed reconstruction position and orientation errors were approximately 0.6 mm and 5 deg., respectively. The physical phantom measurements demonstrated an absolute positional accuracy of (0.78{+-}0.57) mm or less. The {theta} and {phi} angle errors were found to be (5.7{+-}4.9) deg. and (6.0{+-}4.1) deg., respectively, or less when using three projections; with six projections, results were slightly better. The mean registration error was better than 1 mm/6 deg. compared to the measured seed projections. Each test trial converged in 10-20 iterations with computation time of 12-18 min/iteration on a 1 GHz processor. Conclusions: This work describes a novel, accurate, and completely automatic method for reconstructing seed orientations, as well as centroids, from a small number of radiographic projections, in support of intraoperative planning and adaptive replanning. Unlike standard back-projection methods, gIFPM avoids the need to match corresponding seed images on the projections. This algorithm also successfully reconstructs overlapping clustered and highly migrated seeds in the implant. The accuracy of better than 1 mm and 6 deg. demonstrates that gIFPM has the potential to support 2D Task Group 43 calculations in clinical practice.« less
  • Purpose: For African-American patients receiving breast radiotherapy with a bolus, skin darkening can affect the surface visualization when using optical imaging for daily positioning and gating at deep-inspiration breath holds (DIBH). Our goal is to identify a region-of-interest (ROI) that is robust against deteriorating surface image quality due to skin darkening. Methods: We study four patients whose post-mastectomy surfaces are imaged daily with AlignRT (VisionRT, UK) for DIBH radiotherapy and whose surface image quality is degraded toward the end of treatment. To simulate the effects of skin darkening, surfaces from the first ten fractions of each patient are systematically degradedmore » by 25–35%, 40–50% and 65–75% of the total area of the clinically used ROI-ipsilateral-chestwall. The degraded surfaces are registered to the reference surface in six degrees-of-freedom. To identify a robust ROI, three additional reference ROIs — ROI-chest+abdomen, ROI-bilateral-chest and ROI-extended-ipsilateral-chestwall are created and registered to the degraded surfaces. Differences in registration using these ROIs are compared to that using ROI-ipsilateral-chestwall. Results: For three patients, the deviations in the registrations to ROI-ipsilateral-chestwall are > 2.0, 3.1 and 7.9mm on average for 25–35%, 40–50% and 65–75% degraded surfaces, respectively. Rotational deviations reach 11.1° in pitch. For the last patient, registration is consistent to within 2.6mm even on the 65–75% degraded surfaces, possibly because the surface topography has more distinct features. For ROI-bilateral-chest and ROI-extended-ipsilateral-chest registrations deviate in a similar pattern. However, registration on ROI-chest+abdomen is robust to deteriorating image qualities to within 4.2mm for all four patients. Conclusion: Registration deviations using ROI-ipsilateral-chestwall can reach 9.8mm on the 40–50% degraded surfaces. Caution is required when using AlignRT for patients experiencing skin darkening since the accuracy of AlignRT registration deteriorates. To avoid this inaccuracy, we recommend use of ROI-chest+abdomen, on which registration is consistent within 4.2mm even for highly degraded surfaces.« less