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Open Access Research

A computational method using multiresolution for volumetric data integration

Mehmet Ali Akinlar1, Muhammet Kurulay2, Aydin Secer3* and Mehmet Celenk4

Author affiliations

1 Department of Mathematics, Bilecik Seyh Edebali University, Bilecik, 11210, Turkey

2 Department of Mathematics, Yildiz Technical University, Istanbul, 34220, Turkey

3 Department of Mathematical Engineering, Yildiz Technical University, Istanbul, 34220, Turkey

4 School of Electrical Eng. and Computer Science, Ohio University, Athens, OH, 45701-2979, USA

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Citation and License

Boundary Value Problems 2012, 2012:115  doi:10.1186/1687-2770-2012-115

Published: 17 October 2012

Abstract

In this paper, we present a new method for integration of 3-D medical data by utilizing the advantages of 3-D multiresolution analysis and techniques of variational calculus. We first express the data integration problem as a variational optimal control problem where we express the displacement field in terms of wavelet expansions and, secondly, we write the components of the displacement field in terms of wavelet coefficients. We solve this optimization problem with a blockwise descent algorithm. We demonstrate the registration of 3-D brain MR images in the size of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/115/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/115/mathml/M1">View MathML</a> as an application of the present method. Experimental results indicate that the method can integrate 3-D MR images better than only variational or only wavelet-based methods.

MSC: 68U10, 65D18, 65J05, 97N40.

Keywords:
inverse problems; variational optimization; multiresolution; image integration