Minimization Reconstruction Research Articles

TU‐A‐BRB‐01: Groundbreaking 2D and 3D Dosimetry Techniques Using Scintillating Fibers and Tomographic Reconstruction

Purpose: To present the novel concept of tomodosimetry, i.e. the tomographic reconstruction of the dose projections obtained using long scintillating fibers, and its application to 2D and 3D dosimetry. Methods: 2D configuration: 50 scintillating fibers were aligned on a 20cm diameter disk inside a 30cm diameter rotating masonite phantom. 18 dose projections (8 MU each) were measured for each radiation field over a 180 degrees rotation of the phantom. 3D configuration: 128 long scintillating fibers were simulated inside a 20cm diameter, 20cm long cylindrical water‐equivalent phantom. The fibers were placed at various angles on the surface of two cylindrical regions of radius 7.5 and 3.75cm. Using the predicted dose from Pinnacle3, we simulated a 360 degrees rotation of the phantom along its principal axis, collecting the scintillation light from the fibers at each 5 degrees. Both prototypes: the dose in each scintillating fiber plane was reconstructed using a total variation minimization reconstruction iterative algorithm at a resolution of 1×1mm2, and was interpolated in the 3D volume between in each cylindrical plane in the 3D prototype. Results: Absolute measured dose differences in the 2D configuration were on average below 1% in the high dose low gradient region of each field. Absolute doses differences calculated inside the inner cylindrical region were on average of 0.5% and 1.3% of the isocenter dose for a 10×10cm2 field and an IMRT segment, respectively. 3%/3mm gamma tests conducted in both configurations in the isocenter plane achieved a success rate of more than 99% of the dose pixels for the region over 50% of the maximum dose. Conclusions: This work demonstrates the potential of scintillating fiber based tomographic 2D and 3D dosimeters. This methodology allows for millimeter resolution dosimetry in a whole 2D plane or 3D volumes in realtime using only a limited number of detectors.

Super-Resolution Power and Robustness of Compressive Sensing for Spectral Estimation With Application to Spaceborne Tomographic SAR

We address the problem of resolving two closely spaced complex-valued points from N irregular Fourier do- main samples. Although this is a generic super-resolution (SR) problem, our target application is SAR tomography (TomoSAR), where typically the number of acquisitions is N = 10 - 100 and SNR = 0-10 dB. As the TomoSAR algorithm, we introduce Scale-down by LI norm Minimization, Model selection, and Estimation Reconstruction (SL1MMER), which is a spectral estimation algorithm based on compressive sensing, model order selection, and final maximum likelihood parameter estimation. We investigate the limits of SLIMMER concerning the following questions. How accurately can the positions of two closely spaced scatterers be estimated? What is the closest distance of two scat- terers such that they can be separated with a detection rate of 50% by assuming a uniformly distributed phase difference? How many acquisitions N are required for a robust estimation (i.e., for separating two scatterers spaced by one Rayleigh resolution unit with a probability of 90%)? For all of these questions, we provide numerical results, simulations, and analytical approxima- tions. Although we take TomoSAR as the preferred application, the SLIMMER algorithm and our results on SR are generally applicable to sparse spectral estimation, including SR SAR focus- ing of point-like objects. Our results are approximately applicable to nonlinear least-squares estimation, and hence, although it is derived experimentally, they can be considered as a fundamental bound for SR of spectral estimators. We show that SR factors are in the range of 1.5-25 for the aforementioned parameter ranges of N and SNR.

Electron tomography based on a total variation minimization reconstruction technique

The 3D reconstruction of a tilt series for electron tomography is mostly carried out using the weighted backprojection (WBP) algorithm or using one of the iterative algorithms such as the simultaneous iterative reconstruction technique (SIRT). However, it is known that these reconstruction algorithms cannot compensate for the missing wedge. Here, we apply a new reconstruction algorithm for electron tomography, which is based on compressive sensing. This is a field in image processing specialized in finding a sparse solution or a solution with a sparse gradient to a set of ill-posed linear equations. Therefore, it can be applied to electron tomography where the reconstructed objects often have a sparse gradient at the nanoscale. Using a combination of different simulated and experimental datasets, it is shown that missing wedge artefacts are reduced in the final reconstruction. Moreover, it seems that the reconstructed datasets have a higher fidelity and are easier to segment in comparison to reconstructions obtained by more conventional iterative algorithms.

MO-F-214-02: A New, High Resolution 2D Dose Measurement Device Based on a Few Scintillating Fibers and Tomographic Reconstruction

Purpose: To develop and validate a novel type of 2D dosimeter based on the tomographic reconstruction of the dose projections obtained using long scintillating fibers. Methods: 50 parallel scintillating fibers (diameter, 1mm; length, 6 to 20cm) were aligned in a 30cm diameter cylindrical masonite phantom with a 90cm source‐to‐surface distance and a 100cm source‐to‐fibers distance. The fibers were disposed so that the effective detection area of the scintillating fibers was a 20cm diameter disk. Both ends of each scintillating fiber were coupled to clear optical fibers to enable light collection by a single CCDcamera using an f/2, 50mm focal length lens. 7 IMRT segments and 2 square fields were acquired using 18 projections over a 170 degrees rotation of the device. Dose reconstructions were conducted using a total‐variation minimization reconstruction algorithm. 8 monitoring units were programmed for each projection and the reconstructed dose grid pixel resolution was set to 1×1mm,2,. Results: Using a non‐optimized algorithm on a 2GHz CPU, each reconstruction was performed in less than 6 minutes. 3%/3mm gamma tests conducted between the reconstructed IMRT dose distributions and the dose calculated with the treatment planning system Pinnacle,3, were on average successful for 99.6% of the dose pixels for the region over 10% of the maximum dose. For both square fields and the whole summed IMRT field, 100% of the dose pixels were successful to the gamma test. Conclusions: Using tomographic reconstruction on the projections acquired with rotating scintillating fibers, one is able to perform 2D dosimetry of simple and IMRT fields with great accuracy and resolution using only a limited number of scintillating fibers. The underlying concept of tomographic dosimetry and the small number of fibers needed to reconstruct a given 2D dose distribution offer a world of new dosimetric possibility, both applicable to 2D and 3D dosimetry.

Random projections based feature-specific structured imaging

We present a feature-specific imaging system based on the use of structured illumination. The measurements are defined as inner products between the illumination patterns and the object reflectance function, measured on a single photodetector. The illumination patterns are defined using random binary patterns and thus do not employ prior knowledge about the object. Object estimates are generated using L(1)-norm minimization and gradient-projection sparse reconstruction algorithms. The experimental reconstructions show the feasibility of the proposed approach by using 42% fewer measurements than the object dimensionality.

Local tomography property of residual minimization reconstruction with planar integral data

Residual minimization with the well-known conjugate gradient (CG) algorithm has been applied to medical image reconstruction for years. The main advantage of this method is its fast convergence rate. In this paper, we point out that this method has another property-local tomography, when this image reconstruction method is applied to planar integral projections. By local tomography we mean the following: The object is relatively large, the entire object is not sufficiently measured, and the projections are truncated due to a small detector size. However, a small region-of-interest (ROI) is sufficiently measured. The small ROI is able to be exactly reconstructed. This local tomographic property is found for planar integral data only and is not found for line-integral measurements. Iterative local tomography has been applied to cos/spl alpha//r weighted planar integral data through computer simulations and phantom experiments. An efficient projector that models the cos/spl alpha//r weighting factor is also developed.

Boundary-constrained morphological skeleton minimization and skeleton reconstruction

A new algorithm for minimizing a morphological skeleton entitled boundary-constrained skeleton minimization (BCSM), as well as a new algorithm for reconstructing an original image from its minimized skeletal structure termed boundary-constrained skeleton reconstruction (BCSR), are proposed. The new algorithms are shown to reduce data storage requirements from (N+1) binary images represented as separate skeleton subsets with their corresponding indices, to 2 binary images composed of a binary morphological skeleton and its corresponding morphological boundary structure. In addition to a reduction in memory storage, BCSM and BCSR result in substantial savings in computational complexity. The proposed algorithms are evaluated in the context of image analysis and coding, and their performance is compared to previous algorithms proposed by Serra (1982, 1988) and by Maragos and Schafer (1986). Sample evaluations indicate a greater than 22-fold savings in computational requirements and 11-fold reduction in memory requirements. >