One of the main challenges in Computed Tomography is to balance the amount of radiation exposure to the patient at the time of the scan with high image quality. We propose a mathematical model for adaptive Computed Tomography acquisition whose goal is to reduce dosage levels while maintaining high image quality at the same time. The adaptive algorithm iterates between selective limited acquisition and improved reconstruction, with the goal of applying only the dose level needed for sufficient image quality. The theoretical foundation of the algorithm is nonlinear Ridgelet approximation and a discrete form of Ridgelet analysis is used to compute the selective acquisition steps that best capture the image edges. We show experimental results where the adaptive model produces significantly higher image quality, when compared with known non-adaptive acquisition algorithms, for the same number of projection lines.