《Principles Of Magnetic Resonance Imaging》教学Chapter 6.pdfVIP

Chapter 6 Image Reconstruction Onepicture is worth a thousandwords. Oldfolk saying Image synthesis (or reconstruction) is an important topic of tomographic imag- ing because spatial information is encoded into the measured data during the data acquisition step. Depending on how spatial information is encoded into the mea- sured data, the image reconstruction technique necessary can vary considerably. In this chapter, we single out two fundamental image reconstruction problems for detailed discussion: (a) reconstruction from Fourier transform samples, and (b) reconstruction from Radon transform samples. Many practical MRI data ac- quisition schemes lend themselves naturally to one of these two reconstruction problems. For example, if k-space is sampled rectilinearly as shown in Fig. 6.1a, we directly have the first reconstruction problem; if k-space is sampled radially as shown in Fig. 6.1b, we have the second reconstruction problem. For other k- space coverage, signal interpolation is often used to regrid the measured data into one of these two standard formats so that a basic reconstruction algorithm can be applied. This chapter is organized as follows. First, some general issues in image reconstruction are discussed. Then, the theory and algorithms of Fourier recon- struction are described. Finally, image reconstruction from Radon transform data is discussed, starting with a detailed description of the inverse Radon transform, which is followed by an exposition of various practical algorithms. Advanced topics of image reconstruction are presented in Chapter 10. 187 188 Chapter 6 Imag