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

Han, Guanghui; Qu, Gangrong; Wang, Qian

doi:10.1155/2018/5674647

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…According to the definition of the orthogonal complement, R(A) ⊥ = N (A ). Thus, when the linear system ( 9) is inconsistent, the following process is performed [23] A…”

Section: The Block Landweber Iterative Methodsmentioning

confidence: 99%

The Block Landweber Iterative Method for Light Field Reconstruction from a Focal Stack

Liu,

Qu,

Gao

2023

Photonics

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Light field imaging involves reconstructing a 4D light field from a 3D focal stack, which makes it challenging to reconstruct the light field from incomplete projection data. To address this problem, a linear projection system is established to model the focal stack imaging process using discrete refocusing equations. Based on this system, we propose the block Landweber iterative method to find the least-squares solution. This method computes the sparse matrix while iterating, which overcomes the problem of data storage. The 2-norm of the block matrix is utilized as the weighted matrix to normalize every block matrix on an identical scale, delivering an effective relaxation strategy under the convergence condition in the inconsistent case, which yields better reconstruction results and accelerates the convergence speed. The experimental results based on the image quality assessments of reference and non-reference images show that our method achieved better reconstruction results compared to other relevant common methods, even with fewer focal stacks and higher angle resolution.

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“…According to the definition of the orthogonal complement, R(A) ⊥ = N (A ). Thus, when the linear system ( 9) is inconsistent, the following process is performed [23] A…”

Section: The Block Landweber Iterative Methodsmentioning

confidence: 99%

The Block Landweber Iterative Method for Light Field Reconstruction from a Focal Stack

Liu,

Qu,

Gao

2023

Photonics

Self Cite

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show abstract

“…Our method is an example of a general Landweber iterative method [16], for which broad convergence conditions have been established, with…”

Section: Methodsmentioning

confidence: 99%

“…These steps require a choice of λ k before executing the computationally costly matrix-vector multiplications in (15) and (16). By substituting the value of x k+1 from ( 14) into (15) and then ( 15) into ( 16), we re-write the last two steps as:…”

Section: Choice Of Relaxation Coefficientmentioning

confidence: 99%

An Iterative Least Squares Method for Proton CT Image Reconstruction

DeJongh,

DeJongh

2020

Preprint

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Clinically useful proton Computed Tomography images will rely on algorithms to find the three-dimensional proton stopping power distribution that optimally fits the measured proton data. We present a least squares iterative method with many novel features to put proton imaging into a more quantitative framework. These include the definition of a unique solution that optimally fits the protons, the definition of an iteration vector that takes into account proton measurement uncertainties, the definition of an optimal step size for each iteration individually, the ability to simultaneously optimize the step sizes of many iterations, the ability to divide the proton data into arbitrary numbers of blocks for parallel processing and use of graphical processing units, and the definition of stopping criteria to determine when to stop iterating. We find that it is possible, for any object being imaged, to provide assurance that the image is quantifiably close to an optimal solution, and the optimization of step sizes reduces the total number of iterations required for convergence. We demonstrate the use of these algorithms on real data from the ProtonVDA system.

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“…The ISTA method formula is shown in (15). The ISTA method solves Formula (15) through iterative Formula (34), which is shown below

where μ = 1/ L is a suitable step size, and L must be the upper bound of the maximum eigenvalue of A T A [ 48 ], such as

. T α is the shrink operator.…”

Section: Comparison Algorithms and Evaluation Metricsmentioning

confidence: 99%

Regularization Solver Guided FISTA for Electrical Impedance Tomography

Wang

Chen

Wang

et al. 2023

Sensors

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Electrical impedance tomography (EIT) is non-destructive monitoring technology that can visualize the conductivity distribution in the observed area. The inverse problem for imaging is characterized by a serious nonlinear and ill-posed nature, which leads to the low spatial resolution of the reconstructions. The iterative algorithm is an effective method to deal with the imaging inverse problem. However, the existing iterative imaging methods have some drawbacks, such as random and subjective initial parameter setting, very time consuming in vast iterations and shape blurring with less high-order information, etc. To solve these problems, this paper proposes a novel fast convergent iteration method for solving the inverse problem and designs an initial guess method based on an adaptive regularization parameter adjustment. This method is named the Regularization Solver Guided Fast Iterative Shrinkage Threshold Algorithm (RS-FISTA). The iterative solution process under the L1-norm regular constraint is derived in the LASSO problem. Meanwhile, the Nesterov accelerator is introduced to accelerate the gradient optimization race in the ISTA method. In order to make the initial guess contain more prior information and be independent of subjective factors such as human experience, a new adaptive regularization weight coefficient selection method is introduced into the initial conjecture of the FISTA iteration as it contains more accurate prior information of the conductivity distribution. The RS-FISTA method is compared with the methods of Landweber, CG, NOSER, Newton—Raphson, ISTA and FISTA, six different distributions with their optimal parameters. The SSIM, RMSE and PSNR of RS-FISTA methods are 0.7253, 3.44 and 37.55, respectively. In the performance test of convergence, the evaluation metrics of this method are relatively stable at 30 iterations. This shows that the proposed method not only has better visualization, but also has fast convergence. It is verified that the RS-FISTA algorithm is the better algorithm for EIT reconstruction from both simulation and physical experiments.

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

Cited by 7 publications

References 18 publications

The Block Landweber Iterative Method for Light Field Reconstruction from a Focal Stack

The Block Landweber Iterative Method for Light Field Reconstruction from a Focal Stack

An Iterative Least Squares Method for Proton CT Image Reconstruction

Regularization Solver Guided FISTA for Electrical Impedance Tomography

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