Lossless Compression and Linear Recovery of a System Matrix Based on a Polar Adaptive Pixel

The nondestructive characteristics of
$\gamma $
-photon imaging technology make it attractive potential in the industry. However, in industrial detection with a large detection range and high resolution, iteration method, the image reconstruction algorithm which is most widely used, faces the challenge of an overly large system matrix, and the current compression algorithms using the geometric symmetry of the positron emission tomography (PET) system have problems of complex pixel division and recovery mode. Therefore, this study proposes a lossless compression and linear recovery algorithm of the system matrix based on a polar adaptive pixel (LCLR-PAP). Based on the structure of the detection ring and rotation of the circle, the detection field of view (FOV) is designed as a cylinder and the circular slice is divided into several sectors. The pixels are adaptively divided within the sector to realize the lossless compression of the system matrix from the structure, and based on which the angle change of pixels can be converted to matrix transformation to achieve linear recovery. A partial pixel partition is optimized to compensate for the unevenness of the pixel size in the center of the adaptive image. Experiments show that the LCLR-PAP algorithm can provide an efficient solution to the large-scale system matrix compression recovery problem, that is, through a simple and convenient adaptive pixel division with matrix sparsity and axial symmetry, the system matrix can be compressed to less than 100,000th of the original, and realize the lossless compression and fast linear recovery.