In this study, we propose a new graph-theoretical method to simulate guidewire paths inside the carotid artery. The minimum energy guidewire path can be obtained by applying the shortest path algorithm, such as Dijkstra's algorithm for graphs, based on the principle of the minimal total energy. Compared to previous results, experiments of three phantoms were validated, revealing that the first and second phantoms overlap completely between simulated and real guidewires. In addition, 95 % of the third phantom overlaps completely, and the remaining 5 % closely coincides. The results demonstrate that our method achieves 87 and 80 % improvements for the first and third phantoms under the same conditions, respectively. Furthermore, 91 % improvements were obtained for the second phantom under the condition with reduced graph construction complexity.

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In this paper, the generative model is used to introduce the structural properties of the signal to replace the common sparse hypothesis, and a non-convex compressed sensing sparse deviation model based on the generative model ( q -Gen) is proposed. By establishing q variant of the restricted isometry property (q-RIP) and Set-Restricted Eigenvalue Condition (q-S-REC), the error upper bound of the optimal decoder is derived when the recovered signal is within the sparse deviation range of the generator. Furthermore, it is proved that the Gaussian matrix satisfying a certain number of measurements is sufficient to ensure a good recovery for the generating function with high probability. Finally, a series of experiments are carried out to verify the effectiveness and superiority of the q -Gen model.