MRI imaging time can be shortened by speeding up using the compressed sensing method. And it can be used with the conventional parallel imaging method at the same time. One weakness of the compressed sensing method is that it takes a long time to reconstruct the image, although it takes short time to obtain the image data. However, this point has also been shortened to the extent that it does not become a problem in clinical use by the development of image reconstruction systems using GPU units in recent years. The range of applications of the compression sensing method includes 3D imaging (can be accelerated in the plane and slice directions), dynamic imaging (can be accelerated in the time axis direction), cardiac MRI, and upper abdomen with respiratory motion MRI and pediatric patients and other areas that require short-term examinations are assumed.

Phase imaging can achieve higher contrast resolution in measurement of biological soft tissues than attenuation imaging. Recently, simultaneous statistical image reconstruction methods have been reported. The method can reconstruct attenuation, scatter and phase images directly from a set of measured moiré images. We expect that the method has some potentials, e.g., reduction of noise and measurement data. However, the method takes a large computational time. To resolve this issue, we improve the convergence speed of this iterative method. Our method is based on the FBP embedded-type acceleration method developed in attenuation computed tomography. This acceleration method can reconstruct images with a small number of iterations by embedding the FBP structure in the iterative method. The original method was developed to solve the penalized weighted least square problem. We applied the method to solve the maximum likelihood problem. Using the proposed method, we reconstruct a numerical phantom and a real image of mouse bone sample measured by Talbot interferometer. We show the improvement of a convergence speed by the proposed acceleration method.

Radionuclide imaging such as positron emission tomography (PET) and single photon emission computed tomography (SPECT) can provides 3-dimensinal images of various molecular functions by using a device that detects gamma rays emitted from a tracer drug labeled with a radioisotope and CT (computed tomography) technique. Therefore, it plays important roles for current medical care from animal experiments to clinical practice. SPECT is used widely because it is inexpensive and easy to perform although less sensitive than PET. In this tutorial, the basics of SPECT will be serialized three times. In this first paper, I give a summary of SPECT.