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Research Papers

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

[+] Author and Article Information
Wei Huang

School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: whuang47@gatech.edu

Yan Wang

School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: yan.wang@me.gatech.edu

David W. Rosen

School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: david.rosen@me.gatech.edu

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF Computing AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received September 11, 2013; final manuscript received December 20, 2013; published online March 7, 2014. Assoc. Editor: Charlie C.L. Wang.

J. Comput. Inf. Sci. Eng 14(2), 021005 (Mar 07, 2014) (10 pages) Paper No: JCISE-13-1176; doi: 10.1115/1.4026376 History: Received September 11, 2013; Revised December 20, 2013

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.

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Figures

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Fig. 1

The process of coupled surfacelet transform and inverse surfacelet transform

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Fig. 2

Geometric interpretation of surfacelets

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Fig. 3

The full and down-sized images of nano-fiber composites

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Fig. 4

The original nine parallel images of nano-fiber composites for reconstruction

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Fig. 5

The cylinderlet overlapped with a fiber surface has the maximum integral

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Fig. 9

Reconstruction results of rigid fiber boundary constraints

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Fig. 10

Full reconstruction results of rigid fiber boundary constraints in the case of Q=25 × 25 × 3=1875. The error is e = 13.2.

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Fig. 11

Reconstruction results of rigid fiber boundary and inner constraints

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Fig. 12

Reconstruction results of semi-rigid constraints with penalty weights for boundary pixels equal to 1 × 1010 and for inner pixels equal to 10. The error is e = 13.2.

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Fig. 13

Reconstruction results of semi-rigid constraints with penalty weights for boundary pixels equal to 1 × 1010 and for inner pixels equal to 1 × 103. The error is e = 12.9.

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Fig. 14

Reconstruction results of semi-rigid constraints with penalty weights for both boundary and inner pixels equal to 1 × 1010. The error is e = 16.5.

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Fig. 15

Reconstruction results of Quasi-Newton method with line search with fiber boundary constraints

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Fig. 6

Reconstruction results of soft boundary constraints with the least-square method

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Fig. 7

Reconstruction results of soft boundary constraints with the conjugate gradient method

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Fig. 8

Reconstruction results of soft fiber boundary and inner constraints

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Fig. 16

Reconstruction result (the first image only) based on the object-boundary constraint in Kawata and Nalcioglu [6]

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