A positron emission tomography (PET) simulator: an effective way to learn filters with MATLAB

Introduction

The simulator provides handy tools to study filtering technology, e.g., Kalman
filter, ensemble Kalman filter, and $H_{\infty }$ filter. The interface is also reserved for
other estimation technologies, such as expectation-maximization (E-M) and
filtered back projection (FBP) algorithms. It simulates a PET system and
generates the results of the scan (or called sinogram data). After been
processed by a reconstruction algorithm, the result will be the image of the
patient’s body, which is precisely the one that the doctor will observe at the
end of a health check. The standard reconstruction technologies are FBP or E-M.
Recently, the deep learning method dramatically improved image quality. With the
help of the simulator, traditional filtering technologies can be practiced.
Compared with the exercises in the textbook, the simulator has the following
advantages.

• Facility Parameters. The parameters, which are required by the
  algorithms, can be directly retrieved. For example, after typing the predict
  equations and the update equations from a textbook, the result will follow.
  The common mistakes, e.g., mismatched matrix dimensions, will be
  automatically detected by the simulator.

• Bad results but not discouraging. The noise embedded in the PET system
  is non-Gaussian. Although the toolbox can supply a linear version of the PET
  model, the result can still be bad. It keeps our heads clear after the
  textbook shows the beautiful math of the Kalman filter and the elegant
  orthogonal projection behind these equations. There are differences between
  the theoretical hypothesis and the physical system. The simulator also
  preserves interfaces that can formally implement the filters. The results
  from formally implementing and informally implementing can be compared.

• Calculation speed depending on the size of the problem. The simulator
  can generate high-resolution sinogram data; however, the time required by
  reconstructing the image increases significantly. It demonstrates that the
  reconstruction algorithm should be accurate; however, it also requires
  efficiency. A patient suffering cerebral infarct may die after waiting days
  for PET results.