Robust Low-Tubal-Rank Tensor Recovery From Binary Measurements.

Low-rank tensor recovery (LRTR) is a natural extension of low-rank matrix recovery (LRMR) to high-dimensional arrays, which aims to reconstruct an underlying tensor X from incomplete linear measurements [Formula: see text]. However, LRTR ignores the error caused by quantization, limiting its application when the quantization is low-level. In this work, we take into account the impact of extreme quantization and suppose the quantizer degrades into a comparator that only acquires the signs of [Formula: see text]. We still hope to recover X from these binary measurements. Under the tensor Singular Value Decomposition (t-SVD) framework, two recovery methods are proposed-the first is a tensor hard singular tube thresholding method; the second is a constrained tensor nuclear norm minimization method. These methods can recover a real n1×n2×n3 tensor X with tubal rank r from m random Gaussian binary measurements with errors decaying at a polynomial speed of the oversampling factor λ:=m/((n1+n2)n3r). To improve the convergence rate, we develop a new quantization scheme under which the convergence rate can be accelerated to an exponential function of λ. Numerical experiments verify our results, and the applications to real-world data demonstrate the promising performance of the proposed methods.

An improved real-time endovascular guidewire position simulation using shortest path algorithm.

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.