Recently, patch‐based regularisation methods have been a topic for tomographic reconstruction, since they are expected to preserve features within patches. However, conventional patch‐based methods tend to ignore important similarities when the two patches being compared have a large intensity difference, while they share similar features in a scaled domain, which often results in the loss of fine details. In this work, to overcome this problem, the authors measure the similarity using normalised patch (NP) differences as well as unnormalised standard patch (SP) differences. A NP difference is obtained by normalising each patch with respect to its mean value and scaling the difference between the two NPs. The addition of NPs provides great potential to restore non‐piecewise flat regions that are often ignored by SP‐based regularisation methods. To combine the two types of patch differences, they use a method of space‐variant linear combination where the weight controlling the balance between the two types is derived from a transform of the gradient of each pixel location. The authors’ experiments for emission tomography reconstruction demonstrate that the proposed method improves not only the overall reconstruction accuracy for realistic data with the non‐piecewise flat structure, but also the contrast recovery of small structures.

With the introduction of combined positron emission tomography (PET)/computed tomography (CT) or PET/magnetic resonance imaging (MRI) scanners, there is an increasing emphasis on reconstructing PET images with the aid of the anatomical side information obtained from X-ray CT or MRI scanners. In this paper, we propose a new approach to incorporating prior anatomical information into PET reconstruction using the nonlocal regularization method. The nonlocal regularizer developed for this application is designed to selectively consider the anatomical information only when it is reliable. As our proposed nonlocal regularization method does not directly use anatomical edges or boundaries which are often used in conventional methods, it is not only free from additional processes to extract anatomical boundaries or segmented regions, but also more robust to the signal mismatch problem that is caused by the indirect relationship between the PET image and the anatomical image. We perform simulations with digital phantoms. According to our experimental results, compared to the conventional method based on the traditional local regularization method, our nonlocal regularization method performs well even with the imperfect prior anatomical information or in the presence of signal mismatch between the PET image and the anatomical image.

While the ML-EM algorithm for reconstruction for emission tomography is unstable due to the ill-posed nature of the problem. Bayesian reconstruction methods overcome this instability by introducing prior information, often in the form of a spatial smoothness regularizer. More elaborate forms of smoothness constraints may be used to extend the role of the prior beyond that of a stabilizer in order to capture actual spatial information about the object. Previously proposed forms of such prior distributions were based on the assumption of a piecewise constant source distribution. Here, the authors propose an extension to a piecewise linear model-the weak plate-which is more expressive than the piecewise constant model. The weak plate prior not only preserves edges but also allows for piecewise ramplike regions in the reconstruction. Indeed, for the authors' application in SPECT, such ramplike regions are observed in ground-truth source distributions in the form of primate autoradiographs of rCBF radionuclides. To incorporate the weak plate prior in a MAP approach, the authors model the prior as a Gibbs distribution and use a GEM formulation for the optimization. They compare quantitative performance of the ML-EM algorithm, a GEM algorithm with a prior favoring piecewise constant regions, and a GEM algorithm with their weak plate prior. Pointwise and regional bias and variance of ensemble image reconstructions are used as indications of image quality. The authors' results show that the weak plate and membrane priors exhibit improved bias and variance relative to ML-EM techniques.