Chinese Journal of Computers   Full Text
Title	A New PET Reconstruction Method Based on Fourier-Wavelet Moment
Authors	HU Yi-Ning ZHOU Jian LUO Li-Min
Address	(Laboratory of Image Science and Technology, School of Computer Science and Engineering, Southeast University, Nanjing 210096)
Year	2007
Issue	No.12(2164—2172)
Abstract &   Background	Abstract The problem of Positron emission tomography(PET) image reconstruction is well-known ill-posed, thus regularization methods are usually considered to suppress the noise effect. In this paper, a new non-regularization method is proposed, which is a feature-based reconstruction method using Fourier-Wavelet basis. The Fourier-Wavelet basis combines Fourier harmonic and Wavelet function, and provides us with convenience performing both Wavelet and Fourier analysis. In order to obtain the reconstructions, we only have to recover the Fourier-Wavelet moment(FWM) from the measurements. To achieve the FWMs the authors employ iterative method. With the aid of the rotation invariance property of the proposed basis, both the online memory storage and computational costs can be reduced. In addition, the property allows us to generate a Row-Action(RA) like fast convergent algorithm. In experiment, the proposed method is compared with several others. The results suggest that the proposed method offer good reconstruction quality comparable to conventional MAP method. keywords Positron Emission Tomography(PET); reconstruction; wavelet; Fourier; moment background In positron emission tomography (PET) image reconstruction, statistical methods are widely used since Shepp and Vardi introduced MLEM method. Because the problem of PET reconstruction is ill-posed, regularization methods are often used to improve reconstruction quality. To obtain good results, regularization term and parameters should be carefully chosen according to different situation. Such selection often involves interaction. Some literatures suggest using feature-based methods, which reconstruct image without using regularization terms. Milanfar applied Legendre moments to tomography reconstruction. He described a framework for the reconstruction of an image from the maximum likelihood (ML) estimates of its Legendre moments. However, Legendre polynomials are globally defined, as a result, it is not adequate for local feature extraction. Unlike Legendre polynomials, wavelet transform is capable of providing both time and frequency localization. The characteristic of wavelet transform is particularly suited to extract local features. Raheja introduced the multigrid and multiresolution concept for PET image reconstruction using EM algorithm, and furthermore transforms his algorithm to a wavelet based multiresolution EM algorithm by extending the concept of switching resolutions in both image and data spaces. Lee applied wavelet Shrinkage into EM algorithm, in his work, ordered subset (OS) method was employed to accelerate the convergence speed. In this paper Fourier-Wavelet moments (FWM) are used for reconstruction. The relationship between the measurements and the moments is established. Since FWM is rotation invariant, it can be used to reduce the computational cost. A row-action (RA) like block iterative algorithm is proposed to accelerate the convergence rate. In addition, inter-iteration filtering scheme is adopted to improve the reconstruction quality. This research was supported by the National Basic Research Program of China under grant No.2003CB716102, and Program for New Century Excellent Talents in University under grant No.NCET-04-0477.