Development of multispectral scatter correction techniques for high resolution positron emission tomography
PET images acquired with a high resolution scanner based on arrays of small discrete detectors are obtained at the cost of low sensitivity and increased detector scatter. It has been postulated that these limitations can be overcome by using multispectral acquisition whereby the energy information is registered together with the spatial coordinates of detected events. This work is an investigation of multispectral data processing methods for high resolution PET. A photon spectral degradation model is proposed to provide theoretical support for energy-based scatter correction methods. This analytical model supplies a complete physical description of the photon propagation and detection processes in both the spatial and spectral domain. It also helps to bridge the gap between a number of heuristic scatter correction approaches and the underlying physical assumptions. In particular, it is shown that such methods as the dual energy window and multispectral frame-by-frame scatter correction techniques have intrinsic deficiencies which may be responsible for their limited success. The potential of multispectral acquisition for developing energy-dependent scatter correction methods is severely impeded by stochastic fluctuations. Two approaches were investigated to overcome this drawback. In the first one, spectral smoothing is attempted in combination with multispectral normalization of detector efficiency and optimal data pre-processing sequence in order to allow truly energy-dependent data processing on a frame-by-frame basis. In the second approach, a global analysis of the multispectral data set is performed by the principal component analysis for reducing both the variance and dimensionality of the multispectral data. Both approaches provide improved data for further processing. The multispectral frame-by-frame convolution scatter correction protocol is shown to yield inferior performance to that of the convolution scatter correction in one broad window. It is concluded that the approximations made in each energy frame to implement the frame-by-frame approach accumulates errors in the final result. Consequently, the spectral smoothing technique and the implementation of the degradation model in the multiple window approach will have to be revisited to overcome this deficiency. A data processing protocol which combines the use of both spatial and spectral information into one scatter correction method is proposed to exploit multispectral data optimally. The method consists of two consecutive steps: first, optimal noise and data dimensionality reduction, as well as partial suppression of scatter, is achieved by performing the global analysis of the multispectral data set; second, a spatial scatter correction technique, the object scatter subtraction and detector scatter restoration algorithm in this study, is used to correct for the residual scatter contribution in the output of the first step. The relevance of such a correction scheme for multispectral data is demonstrated by its superior performance as compared to conventional spatial scatter correction methods. This global scatter correction approach is promising to fulfill the need for high resolution, high sensitivity and quantitative nuclear medicine imaging. All the techniques developed in this work are readily applicable to multiple energy window acquisition in scintigraphic or SPECT imaging.