An RIP-based evaluation method for candidate next generation cardiac CT architectures with carbon nanotube x-ray source

Despite impressive advances in computed tomography (CT) technology in recent years, there are still critical and immediate needs in cardiac CT in terms of high spatial resolution, high temporal resolution, and low radiation dose. Because carbon nanotube (CNT) x-ray sources can be compactly integrated, this technology can be used for multisource or stationary systems to improve temporal resolution. To avoid x-ray source rotation, lots of source-detector pairs are needed in a stationary CNT-based x-ray system. Limited by space and costs, the number of source-detector pairs cannot be too large, which result in a few-view scan problem. The reconstruction can be modeled as a l ₁-norm minimization problem, which usually can be solved by compressive sensing (CS) based algorithms. To evaluate the data completeness of candidate next generation cardiac CT architectures with CNT x-ray source, and based on the fact that smaller restricted isometry property (RIP) constants lead to a better l₁-norm recovery, we constructed a measurement related to the RIP constants. The results show that the proposed RIP-based evaluation method coincides with the known CT reconstruction theory. This method is simple and easily implemented for different CT scan architectures, and it provides a practical tool to evaluate the data completeness in the framework of l ₁-norm recovery theory without a specific CSbased reconstruction algorithm.