Inverse Surfacelet Transform for Image Reconstruction With Constrained-Conjugate Gradient Methods

2014 ◽  
Vol 14 (2) ◽  
Author(s):  
Wei Huang ◽  
Yan Wang ◽  
David W. Rosen
Keyword(s):  
Image Reconstruction ◽  
Conjugate Gradient ◽  
Gradient Methods ◽  
Optimization Methods ◽  
Transformation Process ◽  
Geometric Constraints ◽  
Least Square ◽  
Reconstruction Methods ◽  
Gradient Based ◽  
Surfacelet Transform

Image reconstruction is the transformation process from a reduced-order representation to the original image pixel form. In materials characterization, it can be utilized as a method to retrieve material composition information. In our previous work, a surfacelet transform was developed to efficiently represent boundary information in material images with surfacelet coefficients. In this paper, new constrained-conjugate-gradient based image reconstruction methods are proposed as the inverse surfacelet transform. With geometric constraints on boundaries and internal distributions of materials, the proposed methods are able to reconstruct material images from surfacelet coefficients as either lossy or lossless compressions. The results between the proposed and other optimization methods for solving the least-square error inverse problems are compared.

Inverse Surfacelet Transform for Image Reconstruction With Prior Knowledge

2013 ◽  
Author(s):  
Wei Huang ◽  
Yan Wang ◽  
David W. Rosen
Keyword(s):  
Image Reconstruction ◽  
Prior Knowledge ◽  
Transformation Process ◽  
Geometric Constraints ◽  
Material Composition ◽  
Reconstruction Methods ◽  
Gradient Based ◽  
Geometric Boundary ◽  
Surfacelet Transform ◽  
Image Pixels

Image reconstruction is the transformation process from some other data forms to image pixels. It can be utilized as a method to retrieve material composition information in materials characterization and design. In our previous work, a so-called surfacelet model was proposed to construct the geometric boundary and internal material distribution of heterogeneous materials at the same time. A surfacelet transform is able to efficiently represent boundary information in images of materials. In this paper, new constrained-conjugate-gradient-based image reconstruction methods are proposed as the inverse surfacelet transform. With geometric constraints on internal boundaries of materials, the proposed method is able to automatically identify the locations and orientations of the internal boundaries based on prior knowledge so as to reconstruct material composition with incomplete data.

scholarly journals A Penalized Linear and Nonlinear Combined Conjugate Gradient Method for the Reconstruction of Fluorescence Molecular Tomography

2007 ◽  
Vol 2007 ◽  
pp. 1-19 ◽  
Author(s):  
Shang Shang ◽  
Jing Bai ◽  
Xiaolei Song ◽  
Hongkai Wang ◽  
Jaclyn Lau
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Reconstruction Algorithms ◽  
Fluorescence Molecular Tomography ◽  
Nonlinear Conjugate Gradient Method ◽  
Gradient Based ◽  
Linear And Nonlinear

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

scholarly journals Estimating the unemployment rate using least square and conjugate gradient methods

2018 ◽  
Vol 7 (2.15) ◽  
pp. 94
Author(s):  
Nur Syarafina Mohamed ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Nur Hamizah Abdul Ghani ◽  
Norhaslinda Zull ◽  
...  
Keyword(s):  
Conjugate Gradient Method ◽  
Unemployment Rate ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Labour Force ◽  
Gradient Methods ◽  
Least Square Method ◽  
Least Square ◽  
Year 2000 ◽  
Quadratic Models

Unemployment rate is one of the major issues among Malaysian citizens. The unemployment rate indicates the percentage of the total workforce who are actively seeking employment and currently unemployed. In this paper, a data of unemployment rate of a state in Malaysia from year 2000 until 2015 is collected. The statistics data is extracted by Labour Force Survey Malaysia (LFSM) which was conducted monthly by using household approach targeted to working ages between 15 to 64 years old. An estimation data for year 2016 can be forecasted by using discrete least square method of numerical analysis and conjugate gradient method in unconstrained optimization. These methods have been chosen based on its simplicity and accuracy. The calculations are based on linear and quadratic models for each the method together with their errors. Results showed that the conjugate gradient method is comparable with the least square method. 

scholarly journals Multiple Linear Regression Model of Rice Production using Conjugate Gradient Methods

MATEMATIKA ◽  
2019 ◽  
Vol 35 (2) ◽  
pp. 229-236
Author(s):  
Nur Idalisa Norddin ◽  
Mohd Rivaie Mohd Ali ◽  
Nurul Hafawati Fadhilah ◽  
Nur Atikah ◽  
Anis Shahida ◽  
...  
Keyword(s):  
Regression Model ◽  
Conjugate Gradient ◽  
Regression Models ◽  
Gradient Methods ◽  
Multiple Linear Regression Model ◽  
Least Square Method ◽  
Rice Production ◽  
Least Square ◽  
Basic Relationship ◽  
Least Square Problem

Regression is one of the basic relationship models in statistics. This paper focuses on the formation of regression models for the rice production in Malaysia by analysing the effects of paddy population, planted area, human population and domestic consumption. In this study, the data were collected from the year 1980 until 2014 from the website of the Department of Statistics Malaysia and Index Mundi. It is well known that the regression model can be solved using the least square method. Since least square problem is an unconstrained optimisation, the Conjugate Gradient (CG) was chosen to generate a solution for regression model and hence to obtain the coefficient value of independent variables.  Results show that the CG methods could produce a good regression equation with acceptable Root Mean-Square Error (RMSE) value.

Robust Parameter Design of Derivative Optimization Methods for Image Acquisition Using a Color Mixer

2015 ◽  
Author(s):  
HyungTae Kim ◽  
SeungTaek Kim ◽  
KyungChan Jin ◽  
Jongseok Kim ◽  
SungHo Lee
Keyword(s):  
Image Quality ◽  
Taguchi Method ◽  
Conjugate Gradient ◽  
Image Acquisition ◽  
Gradient Methods ◽  
Optimization Methods ◽  
Steepest Descent ◽  
Inspection System ◽  
Conjugate Gradient Methods ◽  
Color Mixer

A tuning method was proposed for automatic lighting (auto-lighting) algorithms derived from the steepest descent and conjugate gradient methods. The auto-lighting algorithms maximize the image quality of the industrial machine vision by adjusting multiple-color light emitting diodes (LEDs), usually called color mixers. Searching for the driving condition for achieving maximum sharpness, which influences image quality, using multiple color LEDs, is time-consuming. Hence, the steepest descent and conjugate gradient methods were applied to reduce the searching time for achieving maximum image quality. The relationship between lighting and image quality is multi-dimensional, non-linear, and difficult to describe using mathematical equations. Hence the Taguchi method is actually the only method that can determine the parameters of auto-lighting algorithms. The Taguchi method was applied to an inspection system consisting of an industrial camera, coaxial lens, color mixer, image acquisition device, analog interface board, and semiconductor patterns for target objects. The algorithm parameters were determined using orthogonal arrays and the candidate parameters were selected by increasing the sharpness and decreasing the iterations of the algorithm, which were dependent on the searching time. After conducting retests using the selected parameters, the image quality was almost the same as that in the best-case parameters with a smaller number of iterations. The Taguchi method will be useful in reducing time-consuming tasks and the time required to set up the inspection process in manufacturing.

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