Hyperfixation point-source reconstruction by the maximum entropy on the mean method

Point-source reconstruction arises as an important problem in many applications of nuclear instrumentation. Our main concern is PET image reconstruction for oncology in order to improve the detection of hyperfixation point source as metastasis or to reconstruct an object from a fewer number of measures. The issue is to reach detectability of small objects from noisy data. We propose to perform a statistical reconstruction method, based on the maximum entropy on the mean principle. This method is particularly relevant to solve strongly ill-posed problems. Taking into account statistical data distribution and prior knowledge, it is able to detect small objects from noisy data, which may be angularly or spatially undersampled. As opposed to classical regularisation methods for reconstruction, this method does not imply any spatial smoothing operation. We illustrate the method on simulated noisy angularly undersampled acquisitions