Patch-based low-rank regularization for 4D dynamic CT/PET reconstruction

Abstract

Dynamic and multi-frame medical imaging techniques using the computed tomography (CT) and positron emission tomography (PET) have been used for the specific purposes such as the functional brain kinetic analysis, cardiac cine imaging, respiratory motion and spectral CT. To improve the image quality, dynamic and multi-frame redundant information can be used. However, we need to consider such that the intensity varies over time in the dynamic PET and the deformation occurs in the cardiac CT. To address this issue, many advanced reconstruction algorithms have been developed using various spatio-temporal regularization schemes. Sparsity penalty is one of the popular methods, which minimizes the coefficients in the transform domain such as using the Fourier transform, wavelet transform and principle component analysis. However, one of the problems is that the pixel-based penalty is very sensitive to the intensity variation, which results in the over-smooth image. To overcome this issue, the global low-rank penalty has been used for less sensitive to global intensity variation, which utilizes spatio-temporal correlation of images. However, the global low-rank is difficult to capture the motion structures. Recently, the patch-based method has been developed, which is robust to noise while preserving the image resolution and geometrical structures in motions. By extending previous approaches, we propose a penalized maximum likelihood method using a novel non-convex patch-based low-rank penalty by exploiting the self-similarity of spatio-temporal patches that are collected in dynamic and multi-frame images. Since the similar patches have only a few principle components, it could be the low-rank. Thus, one of the main advantage of the proposed method is that the patch-based low-rank constraint is less sensitive to intensity variation while preserving edge directions and motion components. In the optimization framework, the original cost function consists of the Poisson l...