3D Reconstruction in Magnetic Resonance Imaging

Abstract

This article deals with three-dimensional reconstruction methods of nuclear mag- netic resonance images. The testing images were observed by tomography with basic magnetic fleld of 4.7T at the Institute of Scientiflc Instruments (Academy of Sciences of the Czech Re- public). 10 slices of the testing phantom were acquired. The methods were proposed with the aim of getting utmost information about the shape of the testing phantom. One possible way is to increase the number of the sensed slices, but it implies decreasing of the signal to noise ratio. The second approach is flnding the compromise between the efiective count of slices and the following interpolation of other slices between the sensed ones. The both approaches were compared. The resultant images were segmented by the active contour methods which are based on partial difierential equations solution (1,2). The advantage of these methods is that the images may not be preprocessed before segmentation. The appropriate segmented slices were compared. The following image processing leading to 3D model creation is proposed. The advantages of the nuclear magnetic resonance (NMR) were described in many publications. It is approach to acquisition of spatial data of soft tissues. The main advantage is absolutely the fact of unproved negative efiects of the electromagnetic radiation to human organism subject to prescribed hygienic regulations. Against to other tomographic approaches the magnetic resonance images are with the higher resolution and quality. The observed images of sensed object can be used for three-dimensional model creation after the application of suitable preprocessing methods. The reconstructed object can be useful for example to the better diagnosis in medical sciences, for quantitative or qualitative description of tissues, tumors etc. The requirement is to have utmost slices for the three-dimensional model of sensed tissue. The signal-to-noise ratio (SNR) decreases with increasing the number of slices (1). We have to specify compromises between the number of observed slices and satisfying SNR in images individually. However, if we actually need more slices for the 3D model creation, we can calculate the other images between observed ones. Two basic approaches are described for images interpolation of MR spatial data in this paper. The flrst method is based on ordinary averaging of neighboring pixels intensities with the same position in the frequency domain. We can get the images describing the real scene by Fourier transformation of each slices in the k-space, which we observed by tomography. We can get (2n i 1) images from original n images. This algorithm is repeatable. By the second approach we process directly the data in k-space. There is created a vector of complex numbers by data observing with the same positions in the k-space. Then the frequency domain of this vector is obtained by Fourier transformation (2,3). The frequency domain is extended by zero values for higher frequency part. This extended spectrum is transformed back to the time domain by the inverse Fourier transformation. The length of the obtained vector depends on number of zeros included to frequency spectrum of the original vector. The slices of 4 ∞asks with water were inserted to work space of tomography with the magnetic fleld 4.7T (200MHz for 1 H nuclei) for the testing. This phantom is shown in the Figure 1. 2. OBTAINING OF THE MR IMAGES The images obtained by MR tomography in the time domain (k-space) are then transformed by Fourier transformation to the frequency domain. These images in the frequency domain repre- sent the real scenes. The flrst method interpolates the three-dimensional data in the transformed frequency domain. The second method shows the possibility of data processing and interpolating the three-dimensional data in the original time domain | k-space. We can see in Figure 2 the procedure of scanned spatio-temporal slices processing and the transformation of the slices to the frequency domain, which represents the real scene.