Robust principle component analysis based four-dimensional computed tomography

The purpose of this article for four-dimensional (4D) computed tomography (CT) is threefold. (1) A new spatiotemporal model is presented from matrix perspective with the row dimension in space and the column dimension in time, namely, Robust PCA based 4DCT model (Robust Principle Component Analysis based 4D CT). That is, instead of viewing the 4D object as a temporal collection of three-dimensional (3D) images and looking for local coherence in time or space independently, we perceive it as a mixture of low-rank matrix and sparse matrix to explore the maximum temporal coherence of spatial structure among phases. Here the low-rank matrix corresponds to the “background” or reference state, which is stationary over time or similar in structure; the sparse matrix stands for the “motion” or time-varying component, e.g., heart motion in cardiac imaging, which is often either approximately sparse itself or can be sparsified in the proper basis. Besides 4D CT, this Robust PCA based 4DCT model should be applicable in other imaging problems for motion reduction or/and change detection with the least amount of data, such as multi-energy CT, cardiac MRI, and hyperspectral imaging. (2) A dynamic strategy for data acquisition, i.e., a temporally spiral scheme, is proposed that can potentially maintain the similar reconstruction accuracy with much fewer projections of the data. The key point of this dynamic scheme is to reduce the total number of measurements and hence the radiation dose, by acquiring complementary data in different phases while reducing redundant measurements of the common background structure. (3) An accurate, efficient, yet simple-to-implement algorithm based on split Bregman method is developed for solving the model problem with the sparse representation in tight frames.