Using Radon Transform in Image Reconstruction (original) (raw)

Reflective tomography solved by the inverse Radon transform

HAL (Le Centre pour la Communication Scientifique Directe), 2015

This paper is concerned with imaging a 3D scene from a set of 2D laser images of backscattered intensity. The interaction between an electromagnetic wave and a medium can be understood and modeled in different ways. In the context considered here, the interaction results in a 3D projection of the scene. After inspection in this projection, the reflection data appear as a sum in 3D of local sinograms with severely limited angle view. Therefore, the approach proposed here consists in considering reflection data as an incomplete data set of Radon-kind used in conventional Computerized Tomography (CT). Under this assumption, the use of the reconstruction techniques, such as the well-known filtered backprojection (FBP), provides a 3D-surface reconstruction of the scene from reflective data. Such 3D reconstructions are performed with short computation times. Simulation results using real data in laser tomography attest of the strength and of the relevancy of such an approach.

Local and Global Tomographic Image Reconstruction with Discrete Radon Transform

Computerized Tomography is very practical area of research, wh ich is applicable in many other fields such as material testing imaging etc. In this work we give an inversion formula using discrete convolution back projection algorithm on discrete Radon transform, which makes it faster as interpolation is not required and results are comparable.

Computerized tomography and the Radon transform

2007

We give an overview of some of the mathematical foundations of Computerized Tomography as well as of some of the tools and problems that arise from the mathematical model discussed and its numerical implementation.

Reflective Imaging Solved by the Radon Transform

IEEE Geoscience and Remote Sensing Letters, 2016

This paper is concerned with imaging a 3D scene from a set of 2D laser images of backscattered intensity. The interaction between an electromagnetic wave and a medium can be understood and modeled in different ways. In the context considered here, the interaction results in a 3D projection of the scene. After inspection in this projection, the reflection data appear as a sum in 3D of local sinograms with severely limited angle view. Therefore, the approach proposed here consists in considering reflection data as an incomplete data set of Radon-kind used in conventional Computerized Tomography (CT). Under this assumption, the use of the reconstruction techniques, such as the well-known filtered backprojection (FBP), provides a 3D-surface reconstruction of the scene from reflective data. Such 3D reconstructions are performed with short computation times. Simulation results using real data in laser tomography attest of the strength and of the relevancy of such an approach.

Application of Reconstruction and Optimization Algorithms in Optical Tomography

World Journal of Engineering and Technology, 2020

Optical tomography is a non-invasive technique that uses visible or near infrared radiation to analyze biological tissues. Researchers take immense attention towards advancement in optical tomography because of its low cost and an advantage of providing anatomical information. Based on the information of optical characteristics, forward and inverse problem of tomography are solved. In this research, finite element method is employed for forward problem and gradient-based optimization algorithm is developed for inverse problem of optical tomography. It is found from simulations that information about imaging is processed more distinctly and in less computational time. Normal and abnormal conditions in imaging are readily distinguished. Simulations are carried out in Matlab. Different scenarios are developed and are simulated to validate the performance of reconstruction and optimization algorithms in optical tomography.

DEVELOPMENT OF DETERMINISTIC AND STOCHASTIC ALGORITHMS FOR INVERSE PROBLEMS OF OPTICAL TOMOGRAPHY

A semi log plot of number of nodes (unknown parameters) versus reconstruction time per frame using methods (given in the legend) (Tab. (3.1)). Polynomial fits corresponding to each method (Appendix AII) are also plotted in this figure. 3.7 (a) An example of reconstructed dynamic data set using SVD method. Corresponding time points are shown on top of the each figure. (b) Recovered a  contrast (maximum value in the target region) versus time. 3.8 Reconstructed a  distributions using (a) nonlinear (b) linear iterative (c) SVD (d) linear efficient, and (e) SVD efficient methods with 1% noise in the data for two inhomogeneities. Flowchart: Flowchart of implementation steps. 4.1 The cross-sectional plots through the center of the inclusion of the images List of Figures xii shown in Fig. (4.2) 4.2 The reference and recovered gray-level a  images (a) Reference, (b), (c), and (d) are respectively obtained from BS, DBS-B and DBS filters 67 4.3 Pseudo-time evolution of the parameters from BS, DBS-B and DBS filters for an absorbing object with one inclusion. (a) h, (b) r and (c)  of the recovered inclusion. 4.4a (a) The recovered gray-level a  images for the two inhomogeneity case: (a) Reference, (b) from the BS and (c) from the DBS filter. 68 4.4b Pseudo-time evolution of the parameters, in the two inclusions, estimated through the BS and DBS filters: (a) h, (b) r and (c)  69 4.5 Time history of RMSE of parameters: (a) h, (b) r and (c)  70 4.6 Time history of sample variance of parameters: (a) h, (b) r and (c)  71 4.7 Reconstruction from experimental data: the evolution of parameters (a) h, (b) r and (c)  estimated through BS, DBS and DBS-B filters 72 4.8 The reconstructed gray-level images from experimental data, using (a) BS, (b) DBS and (c) DBS-B filters. 73 5.1 Reconstruction of absorption coefficient for a phantom with two inhomogeneities using (b) PD-EnKF and (c) Gauss-Newton method where (a) is the reference. 86 5.2 Parameters estimated through PD-EnKF and GN method for a phantom with two inhomogeneities (a) h, and (b) 0, 0 (sgn(())) abs c real c  and (c) 1, 1 (sgn(())) abs c real c   86-87 5.3 Reconstruction of absorption coefficient for an annular ring shaped phantom using (b) PD-EnKF and (c) GN method where (a) is the reference. 87 5.4 Recovery of absorption coefficient for a dumbbell shaped phantom using (b) PD-EnKF and (c) GN method where (a) is the reference. 88 5.5 The reconstructed gray level image corresponding to the experimental data using (a) PD-EnKF and (b) GN method 89 5.6 The parameters estimated through PD-EnKF from the experimental data (a) h and (b) 0,abs c 90 5.7 Reference figure for Figs. 5.8 and 5.9. 91 5.8 (a) Reconstruction through EnKF; (b) reconstruction through GN algorithm; (c) CS through the insonified region along y-axis; (d) convergence of parameters (EnKF) (e) L 2 error norm, for  =4 time samples when the GN algorithm is used with 1% noisy data. 91-92 5.9 (a) Reconstructed figure through EnKF, (b) Reconstructed figure through brute-force (c) CS through the insonification region along y-axis, (d) Convergence of parameters (EnKF) (e) L2 error norm, for  = 4 time samples with CDE for 3% noise. 92-93 5.10 (a) Reference, (b) Reconstructed figure through EnKF, (c) Reconstructed figure through brute-force, (d) CS through the insonification region along yaxis, (e) Convergence of parameters (EnKF), (f) L2 error norm, for  = 4 time samples with CDE for 1% noise. 93-94 6.1 Object and meshing used for 3D forward problem, showing the arrangement brute force EVP    when solving a forward 2-D problem. 106

Reconstruction of tomographic images using analog projections and the digital Radon transform

Linear Algebra and its Applications, 2001

The digital Radon transform (DRT) can be adapted to reconstruct images from analog projection data. This new technique is a variation of the conventional back-projection method. It requires no pre-filtering of the projection data, straightforward 1D linear interpolation and some simple sorting of projection samples. The DRT enables the use of a form of block-data copy for the reconstruction, which is fast in comparison to the usual methods of back-projection. To obtain reconstructed images of high quality, further intrinsic interpolation is required; the reconstructed image size has to be several times larger than the number of projection samples. We describe an algorithm to convert analog projection data into a form suitable to apply the DRT. We compare the performance of the "standard" DRT and a hybrid version of the DRT to some conventional reconstruction algorithms.

Numerical inversion of a broken ray transform arising in single scattering optical tomography

2016

The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the body to recover its interior features. The mathematical model of SSOT is based on the broken ray (or V-line Radon) transform (BRT), which puts into correspondence to an image function its integrals along V-shaped piecewise linear trajectories. The process of image reconstruction in SSOT requires inversion of that transform. We implement numerical inversion of a broken ray transform in a disc with partial radial data. Our method is based on a relation between the Fourier coefficients of the image function and those of its BRT recently discovered by Ambartsoumian and Moon. The numerical algorithm requires solution of ill-conditioned matrix problems, which is accomplished using a half-rank truncated singular value decomposition method. Several numerica...