scholarly journals Expansion of the Nodal-Adjoint Method for Simple and Efficient Computation of the 2D Tomographic Imaging Jacobian Matrix

Sensors ◽  
2021 ◽  
Vol 21 (3) ◽  
pp. 729
Author(s):  
Samar Hosseinzadegan ◽  
Andreas Fhager ◽  
Mikael Persson ◽  
Shireen Geimer ◽  
Paul Meaney
Keyword(s):  
Adjoint Method ◽  
Jacobian Matrix ◽  
Imaging System ◽  
Computational Cost ◽  
Computation Time ◽  
Dipole Approximation ◽  
Discrete Dipole Approximation ◽  
Efficient Computation ◽  
Reconstruction Algorithms ◽  
Reconstruction Process

This paper focuses on the construction of the Jacobian matrix required in tomographic reconstruction algorithms. In microwave tomography, computing the forward solutions during the iterative reconstruction process impacts the accuracy and computational efficiency. Towards this end, we have applied the discrete dipole approximation for the forward solutions with significant time savings. However, while we have discovered that the imaging problem configuration can dramatically impact the computation time required for the forward solver, it can be equally beneficial in constructing the Jacobian matrix calculated in iterative image reconstruction algorithms. Key to this implementation, we propose to use the same simulation grid for both the forward and imaging domain discretizations for the discrete dipole approximation solutions and report in detail the theoretical aspects for this localization. In this way, the computational cost of the nodal adjoint method decreases by several orders of magnitude. Our investigations show that this expansion is a significant enhancement compared to previous implementations and results in a rapid calculation of the Jacobian matrix with a high level of accuracy. The discrete dipole approximation and the newly efficient Jacobian matrices are effectively implemented to produce quantitative images of the simplified breast phantom from the microwave imaging system.

scholarly journals A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Samar Hosseinzadegan ◽  
Andreas Fhager ◽  
Mikael Persson ◽  
Paul Meaney
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Breast Imaging ◽  
Imaging System ◽  
Dipole Moments ◽  
Dipole Approximation ◽  
Discrete Dipole Approximation ◽  
Two Dimensional ◽  
Iterative Solver ◽  
The Matrix

We introduce the discrete dipole approximation (DDA) for efficiently calculating the two-dimensional electric field distribution for our microwave tomographic breast imaging system. For iterative inverse problems such as microwave tomography, the forward field computation is the time limiting step. In this paper, the two-dimensional algorithm is derived and formulated such that the iterative conjugate orthogonal conjugate gradient (COCG) method can be used for efficiently solving the forward problem. We have also optimized the matrix-vector multiplication step by formulating the problem such that the nondiagonal portion of the matrix used to compute the dipole moments is block-Toeplitz. The computation costs for multiplying the block matrices times a vector can be dramatically accelerated by expanding each Toeplitz matrix to a circulant matrix for which the convolution theorem is applied for fast computation utilizing the fast Fourier transform (FFT). The results demonstrate that this formulation is accurate and efficient. In this work, the computation times for the direct solvers, the iterative solver (COCG), and the iterative solver using the fast Fourier transform (COCG-FFT) are compared with the best performance achieved using the iterative solver (COCG-FFT) in C++. Utilizing this formulation provides a computationally efficient building block for developing a low cost and fast breast imaging system to serve under-resourced populations.

scholarly journals Increasing the Performance of the Iterative Computed Tomography Image Reconstruction Algorithms

2020 ◽  
Vol 23 (2) ◽  
pp. 194-203
Author(s):  
Shimaa Abdulsalam Khazal ◽  
Mohammed Hussein Ali
Keyword(s):  
Computed Tomography ◽  
Image Reconstruction ◽  
Iterative Algorithms ◽  
Computation Time ◽  
Ct Imaging ◽  
Reconstruction Technique ◽  
Reconstruction Algorithms ◽  
Reconstruction Process ◽  
Simulation Results ◽  
Reconstruction Time

Computed tomography (CT) imaging is an important diagnostic tool. CT imaging facilitates the internal rendering of a scanned object by measuring the attenuation of beams of X-ray radiation. CT employs a mathematical technique of image reconstruction; those techniques are classified as; analytical and iterative. The iterative reconstruction (IR) methods have been proven to be superior over the analytical methods, but due to their prolonged reconstruction time, those methods are excluded from routine use in clinical applications. In this paper the reconstruction time of an IR algorithm is minimized through the employment of an adaptive region growing segmentation method that focuses the image reconstruction process on a specified region, thus ignoring unwanted pixels that increase the computation time. This method is tested on the iterative algebraic reconstruction technique (ART) algorithm. Some phantom images are used in this paper to demonstrate the effects of the segmentation process. The simulation results are executed using MATLAB (version R2018b) programming language, and a computer system with the following specifications: CPU core i7 (2.40 GHz) for processing. Simulation results indicate that this method will reduce the reconstruction time of the iterative algorithms, and will enhance the quality of the reconstructed image.

scholarly journals Correction for the Partial Volume Effects (PVE) in Nuclear Medicine Imaging: A Post-Reconstruction Analytic Method

2021 ◽  
Vol 11 (14) ◽  
pp. 6460
Author(s):  
Fabio Di Martino ◽  
Patrizio Barca ◽  
Eleonora Bortoli ◽  
Alessia Giuliano ◽  
Duccio Volterrani
Keyword(s):  
Nuclear Medicine ◽  
Imaging System ◽  
Tomographic Reconstruction ◽  
Mathematical Expression ◽  
Reconstruction Algorithm ◽  
Volume Effect ◽  
Nuclear Medicine Imaging ◽  
Theoretical Derivation ◽  
Reconstruction Process ◽  
Partial Volume

Quantitative analyses in nuclear medicine are increasingly used, both for diagnostic and therapeutic purposes. The Partial Volume Effect (PVE) is the most important factor of loss of quantification in Nuclear Medicine, especially for evaluation in Region of Interest (ROI) smaller than the Full Width at Half Maximum (FWHM) of the PSF. The aim of this work is to present a new approach for the correction of PVE, using a post-reconstruction process starting from a mathematical expression, which only requires the knowledge of the FWHM of the final PSF of the imaging system used. After the presentation of the theoretical derivation, the experimental evaluation of this method is performed using a PET/CT hybrid system and acquiring the IEC NEMA phantom with six spherical “hot” ROIs (with diameters of 10, 13, 17, 22, 28, and 37 mm) and a homogeneous “colder” background. In order to evaluate the recovery of quantitative data, the effect of statistical noise (different acquisition times), tomographic reconstruction algorithm with and without time-of-flight (TOF) and different signal-to-background activity concentration ratio (3:1 and 10:1) was studied. The application of the corrective method allows recovering the loss of quantification due to PVE for all sizes of spheres acquired, with a final accuracy less than 17%, for lesion dimensions larger than two FWHM and for acquisition times equal to or greater than two minutes.

scholarly journals Partial aperture imaging system based on sparse point spread holograms and nonlinear cross-correlations

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Angika Bulbul ◽  
Joseph Rosen
Keyword(s):  
Structural Changes ◽  
Imaging System ◽  
Current System ◽  
Three Dimensional ◽  
Phase Mask ◽  
Coded Aperture ◽  
Space Telescopes ◽  
Reconstruction Process ◽  
Cross Correlations ◽  
Equivalent Systems

AbstractPartial aperture imaging system (PAIS) is a recently developed concept in which the traditional disc-shaped aperture is replaced by an aperture with a much smaller area and yet its imaging capabilities are comparable to the full aperture systems. Recently PAIS was demonstrated as an indirect incoherent digital three-dimensional imaging technique. Later it was successfully implemented in the study of the synthetic marginal aperture with revolving telescopes (SMART) to provide superresolution with subaperture area that was less than one percent of the area of the full synthetic disc-shaped aperture. In the study of SMART, the concept of PAIS was tested by placing eight coded phase reflectors along the boundary of the full synthetic aperture. In the current study, various improvements of PAIS are tested and its performance is compared with the other equivalent systems. Among the structural changes, we test ring-shaped eight coded phase subapertures with the same area as of the previous circular subapertures, distributed along the boundary of the full disc-shaped aperture. Another change in the current system is the use of coded phase mask with a point response of a sparse dot pattern. The third change is in the reconstruction process in which a nonlinear correlation with optimal parameters is implemented. With the improved image quality, the modified-PAIS can save weight and cost of imaging devices in general and of space telescopes in particular. Experimental results with reflective objects show that the concept of coded aperture extends the limits of classical imaging.

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