The Results of the Sub-Pixel Efficacy Region Based Lagrange and Sinc Interpolation Functions

The Results of the Sub-Pixel Efficacy Region Based Lagrange and Sinc Interpolation Functions

Carlo Ciulla (Lane College, USA)
DOI: 10.4018/978-1-60566-202-2.ch019
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Abstract

This chapter presents results obtained processing the MRI dataset with classic and SRE-based models of one dimensional Lagrange and Sinc interpolation functions. The presentation is consistent with chapters VIII, XI, and XV where bivariate linear, trivariate linear and B-Splines’ results were reported and consists of a compilation that is both quantitative and qualitative.
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Validation Methodology And Mri Dataset

The validation methodology adopted to validate both SRE-based Lagrange SRE-based Sinc interpolation functions is same as that reported earlier (Ciulla & Deek, 2006) (section 3.1) and same as that seen previously in Section IV of this book for one dimensional quadratic and cubic SRE-based B-Splines. As previously clarified, the term processed will be used to indicate that the image was motion corrected and interpolated. When using the misplacement x0 the image is termed as processed with classic Lagrange and Sinc interpolation functions as per equations (2) and (30) (chapter 18) respectively. When using the novel re-sampling location xr0 obtained from equation (26) and equations (43), (44) of chapter 18 the image is termed as processed with Lagrange and Sinc SRE-based interpolation functions respectively.

The misplacements were all along the x coordinate at steps of: (i) 0.01, (ii) 0.0025, (iii) 0.00001 and their range were: (i) [0, 0.99], (ii) [0, 0.2475], (iii) [0, 0.00099], all fractions of the pixel size. The image database (T1 MRI, T2 MRI and functional MRI) used for the validation of the SRE-based interpolation functions is the same as that used in Part III of the book for the study of the SRE-based B-Splines and for convenience to the reader the MRI images’ resolution and matrix size are herein recalled:

  • T1 MRI (T1-MRI-230 and T1-MRI-450). Matrix resolution: 176 x 208 with 1.00 x 1.00 mm of pixel size, with 75 slices and an inter-slice resolution of 1.00 mm.

  • T2 MRI: matrix resolution was 177 x 182 with 1.00 x 1.00 mm of pixel size, with 19 slices and an inter-slice resolution of 1.00 mm.

  • Functional MRI (fMRI-TS1). Matrix resolution was 128 x 128 with 1.72 x 1.72 mm of pixel size, with 20 slices and an inter-slice resolution of 1.72 mm.

Also, this chapter constitutes of an extension of the investigation reported earlier (Ciulla & Deek, 2006) where a presentation of the capability of the SRE-based Lagrange interpolation function was reported on a variety of imaging modalities including cellular imaging. This section of the book focuses on the presentation of results obtained employing T1-MRI (T1-MRI-230 and T1-MRI-450), T2-MRI and functional MRI (fMRI-TS1) data sets.

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