scholarly journals Weighting Algorithm and Relaxation Strategies of the Landweber Method for Image Reconstruction

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
Guanghui Han ◽  
Gangrong Qu ◽  
Qian Wang
Keyword(s):  
Image Reconstruction ◽  
Iterative Algorithms ◽  
Projection Data ◽  
High Quality ◽  
Ill Posed ◽  
High Resolution Images ◽  
Landweber Method ◽  
Weighting Methods ◽  
Limited Angle

The iterative approach is important for image reconstruction with ill-posed problem, especially for limited angle reconstruction. Most of iterative algorithms can be written in the general Landweber scheme. In this context, appropriate relaxation strategies and appropriately chosen weights are critical to yield reconstructed images of high quality. In this paper, based on reducing the condition number of matrix ATA, we find one method of weighting matrices for the general Landweber method to improve the reconstructed results. For high resolution images, the approximate iterative matrix is derived. And the new weighting matrices and corresponding relaxation strategies are proposed for the general Landweber method with large dimensional number. Numerical simulations show that the proposed weighting methods are effective in improving the quality of reconstructed image for both complete projection data and limited angle projection data.

Ultra-limited-angle CT image reconstruction algorithm based on reweighting and edge-preserving

2022 ◽  
pp. 1-13
Author(s):  
Lei Shi ◽  
Gangrong Qu ◽  
Yunsong Zhao
Keyword(s):  
Image Reconstruction ◽  
Condition Number ◽  
Reconstruction Algorithm ◽  
Projection Data ◽  
Ct Image ◽  
Reconstruction Algorithms ◽  
Edge Preserving ◽  
Image Reconstruction Algorithm ◽  
Ct Image Reconstruction ◽  
Limited Angle

BACKGROUND: Ultra-limited-angle image reconstruction problem with a limited-angle scanning range less than or equal to π 2 is severely ill-posed. Due to the considerably large condition number of a linear system for image reconstruction, it is extremely challenging to generate a valid reconstructed image by traditional iterative reconstruction algorithms. OBJECTIVE: To develop and test a valid ultra-limited-angle CT image reconstruction algorithm. METHODS: We propose a new optimized reconstruction model and Reweighted Alternating Edge-preserving Diffusion and Smoothing algorithm in which a reweighted method of improving the condition number is incorporated into the idea of AEDS image reconstruction algorithm. The AEDS algorithm utilizes the property of image sparsity to improve partially the results. In experiments, the different algorithms (the Pre-Landweber, AEDS algorithms and our algorithm) are used to reconstruct the Shepp-Logan phantom from the simulated projection data with noises and the flat object with a large ratio between length and width from the real projection data. PSNR and SSIM are used as the quantitative indices to evaluate quality of reconstructed images. RESULTS: Experiment results showed that for simulated projection data, our algorithm improves PSNR and SSIM from 22.46db to 39.38db and from 0.71 to 0.96, respectively. For real projection data, our algorithm yields the highest PSNR and SSIM of 30.89db and 0.88, which obtains a valid reconstructed result. CONCLUSIONS: Our algorithm successfully combines the merits of several image processing and reconstruction algorithms. Thus, our new algorithm outperforms significantly other two algorithms and is valid for ultra-limited-angle CT image reconstruction.

scholarly journals A Novel Blind Restoration and Reconstruction Approach for CT Images Based on Sparse Representation and Hierarchical Bayesian-MAP

Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 174
Author(s):  
Sun ◽  
Zhang ◽  
Li ◽  
Meng
Keyword(s):  
Image Reconstruction ◽  
Radiation Dose ◽  
Image Restoration ◽  
Sparse Representation ◽  
Iterative Reconstruction ◽  
Model Parameters ◽  
Projection Data ◽  
Ct Image ◽  
High Quality ◽  
Ct Image Reconstruction

Computed tomography (CT) image reconstruction and restoration are very important in medical image processing, and are associated together to be an inverse problem. Image iterative reconstruction is a key tool to increase the applicability of CT imaging and reduce radiation dose. Nevertheless, traditional image iterative reconstruction methods are limited by the sampling theorem and also the blurring of projection data will propagate unhampered artifact in the reconstructed image. To overcome these problems, image restoration techniques should be developed to accurately correct a wide variety of image degrading effects in order to effectively improve image reconstruction. In this paper, a blind image restoration technique is embedded in the compressive sensing CT image reconstruction, which can result in a high-quality reconstruction image using fewer projection data. Because a small amount of data can be obtained by radiation in a shorter time, high-quality image reconstruction with less data is equivalent to reducing radiation dose. Technically, both the blurring process and the sparse representation of the sharp CT image are first modeled as a serial of parameters. The sharp CT image will be obtained from the estimated sparse representation. Then, the model parameters are estimated by a hierarchical Bayesian maximum posteriori formulation. Finally, the estimated model parameters are optimized to obtain the final image reconstruction. We demonstrate the effectiveness of the proposed method with the simulation experiments in terms of the peak signal to noise ratio (PSNR), and structural similarity index (SSIM).

scholarly journals High Resolution Imaging of Compact Radio Sources by Gridding with Regularization

1998 ◽  
Vol 164 ◽  
pp. 411-412 ◽  
Author(s):  
S. F. Likhachev ◽  
R. M. Hjellming
Keyword(s):  
High Resolution ◽  
Image Reconstruction ◽  
Radio Source ◽  
Radio Sources ◽  
High Resolution Imaging ◽  
Traditional Methods ◽  
Compact Radio Source ◽  
Ill Posed ◽  
Resolution Imaging

AbstractThe problem of VLBI image reconstruction is a classical example of an ill-posed problem. A new procedure of gridding with regularization has been developed. This procedure was used in traditional methods (CLEAN, Hybrid) to improve the quality of compact radio source images. A few sources (GRO J1655–40, RY Scuti and Cyg X-1), observed with the VLA and VLBA, were processed with this procedure.

Preliminary Results of Integrating Tikhonov’s Regularization in Forward-Backward Time-Stepping Technique for Object Detection

2016 ◽  
Vol 833 ◽  
pp. 170-175 ◽  
Author(s):  
Andrew Sia Chew Chie ◽  
Kismet Anak Hong Ping ◽  
Yong Guang ◽  
Ng Shi Wei ◽  
Nordiana Rajaee
Keyword(s):  
Image Reconstruction ◽  
Inverse Scattering ◽  
Time Domain ◽  
Regularization Method ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Time Stepping ◽  
Ill Posed ◽  
Tikhonov’S Regularization

The inverse scattering in time domain known as Forward-Backward Time-Stepping (FBTS) technique is applied to determine the sizes, shape and location of the embedded objects. Tikhonov’s regularization method has been proposed in order to improve or solve the ill-posed of FBTS inverse scattering problem. The reconstructed results showed that FBTS technique can detect the presence of embedded objects. The reconstructed results of FBTS technique utilizing with the Tikhonov’s regularization method shown better results than the results only applied FBTS technique. Tikhonov’s regularization combined with FBTS technique to improve the quality of image reconstruction.

Anisotropic structure property based image reconstruction method for limited-angle computed tomography

2021 ◽  
pp. 1-24
Author(s):  
Changcheng Gong ◽  
Li Zeng
Keyword(s):  
Computed Tomography ◽  
Image Reconstruction ◽  
Projection Data ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Anisotropic Structure ◽  
Structure Property ◽  
Image Reconstruction Method ◽  
Ct Data ◽  
Limited Angle

Limited-angle computed tomography (CT) may appear in restricted CT scans. Since the available projection data is incomplete, the images reconstructed by filtered back-projection (FBP) or algebraic reconstruction technique (ART) often encounter shading artifacts. However, using the anisotropy property of the shading artifacts that coincide with the characteristic of limited-angle CT images can reduce the shading artifacts. Considering this concept, we combine the anisotropy property of the shading artifacts with the anisotropic structure property of an image to develop a new algorithm for image reconstruction. Specifically, we propose an image reconstruction method based on adaptive weighted anisotropic total variation (AwATV). This method, termed as AwATV method for short, is designed to preserve image structures and then remove the shading artifacts. It characterizes both of above properties. The anisotropy property of the shading artifacts accounts for reducing artifacts, and the anisotropic structure property of an image accounts for preserving structures. In order to evaluate the performance of AwATV, we use the simulation projection data of FORBILD head phantom and real CT data for image reconstruction. Experimental results show that AwATV can always reconstruct images with higher SSIM and PSNR, and smaller RMSE, which means that AwATV enables to reconstruct images with higher quality in term of artifact reduction and structure preservation.

A preconditioned landweber iteration scheme for the limited-angle image reconstruction

2021 ◽  
pp. 1-19
Author(s):  
Lei Shi ◽  
Gangrong Qu
Keyword(s):  
Image Reconstruction ◽  
Linear System ◽  
Condition Number ◽  
Small Angle ◽  
Practical Importance ◽  
Iteration Scheme ◽  
Normal Equation ◽  
Projection Data ◽  
Reconstruction Problem ◽  
Limited Angle

BACKGROUND: The limited-angle reconstruction problem is of both theoretical and practical importance. Due to the severe ill-posedness of the problem, it is very challenging to get a valid reconstructed result from the known small limited-angle projection data. The theoretical ill-posedness leads the normal equation A T Ax = A T b of the linear system derived by discretizing the Radon transform to be severely ill-posed, which is quantified as the large condition number of A T A. OBJECTIVE: To develop and test a new valid algorithm for improving the limited-angle image reconstruction with the known appropriately small angle range from [ 0 , π 3 ] ∼ [ 0 , π 2 ] . METHODS: We propose a reweighted method of improving the condition number of A T Ax = A T b and the corresponding preconditioned Landweber iteration scheme. The weight means multiplying A T Ax = A T b by a matrix related to A T A, and the weighting process is repeated multiple times. In the experiment, the condition number of the coefficient matrix in the reweighted linear system decreases monotonically to 1 as the weighting times approaches infinity. RESULTS: The numerical experiments showed that the proposed algorithm is significantly superior to other iterative algorithms (Landweber, Cimmino, NWL-a and AEDS) and can reconstruct a valid image from the known appropriately small angle range. CONCLUSIONS: The proposed algorithm is effective for the limited-angle reconstruction problem with the known appropriately small angle range.

An Effective Regularization Method for Image Super Resolution

2011 ◽  
Vol 219-220 ◽  
pp. 1411-1414
Author(s):  
En Wei Zheng ◽  
Xian Jun Wang
Keyword(s):  
Super Resolution ◽  
License Plate ◽  
Reconstruction Method ◽  
Ill Posed ◽  
High Resolution Images ◽  
Image Super Resolution ◽  
Sr Reconstruction ◽  
Real Traffic ◽  
Reconstruction Model

In this paper, we propose a new super resolution (SR) reconstruction method to handle license plate numbers of vehicles in real traffic videos. Recently, SR reconstruction shemes based on regularization have been demonstrated to be effective because SR reconstrction is an ill-posed problem. Working within this promising framework, the residual data (RD) term can be weighted according to the differences among the observed LR images in the SR reconstruction model. Moreover, L1 norm is used to measure the RD term in order to improve the robustness of our method. Experiments show the proposed method improves the subjective visual quality of the high resolution images.

AN IMPROVED 3DRP PET IMAGE RECONSTRUCTION METHOD WITH REBINNED DIRECT IMAGE ESTIMATE

2006 ◽  
Vol 18 (05) ◽  
pp. 237-245
Author(s):  
WEI-MIN JENG ◽  
HSUAN-HUI WANG
Keyword(s):  
Image Reconstruction ◽  
Image Quality ◽  
Three Dimensional ◽  
Simulation Software ◽  
Direct Image ◽  
Projection Data ◽  
Reconstruction Method ◽  
Two Dimensional ◽  
Dimensional Image

The quality of traditional two-dimensional image reconstruction for PET has been efficiently improved by three-dimensional image reconstruction, but the sensitivity of the data and the quality of the image are restricted by the limit of modality physics. In analytical image reconstruction algorithm, 3DRP method compensates the unmeasured events by forward projection based on the initial direct image estimate. However, the original 3DRP method merely depends on the parallel projections without taking into account the oblique projections. In our proposed 3DRP-SSRB method, we improve the first image estimate by incorporating the rebinned oblique data. SSRB method was used to perform the rebinning operation to make uses of the oblique projection data to improve the sensitivity information. And then project the improved image estimate forward and reconstruct the final image. Conflicting parameters of reconstructed image quality of 3DRP are experimented by simulated three-dimensional phantom study with regard to both system sensitivity and image quality factors. PET simulation software package was used to conduct the experiment along with the MATLAB software to evaluate the effectiveness of two-dimensional FBP, 3DRP, and our proposed 3DRP-SSRB methods. The result demonstrated its better image quality by having better mean squared error numbers in most of output image slices.

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