Tao Qian

You Gao, Tao Qian, Vladimir Temlyakov et al.

As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable influence to the rational approximation of one complex variable and phase retrieving problems, etc. In a recent paper, Qian developed 2D-AFDs for treating square images as the essential boundary of the 2-torus embedded into the space of two complex variables. This paper studies the numerical aspects of multi-dimensional AFDs, and in particular 2D-AFDs, which mainly include (i) Numerical algorithms of several types of 2D-AFDs in relation to image representation; (ii) Perform experiments for the algorithms with comparisons between 5 types of image reconstruction methods in the Fourier category; and (iii) New and sharper estimations for convergence rates of orthogonal greedy algorithm and pre-orthogonal greedy algorithm. The comparison shows that the 2D-AFD methods achieve optimal results among the others.

Lasse Hansen, Wiebke Heyer, Christoph Großbröhmer et al.

Medical image registration is critical for clinical applications, and fair benchmarking of different methods is essential for monitoring ongoing progress. To date, the Learn2Reg 2020-2023 challenges have released several complementary datasets and established metrics for evaluations. However, these editions did not capture all aspects of the registration problem, particularly in terms of modality diversity and task complexity. To address these limitations, the 2024 edition introduces three new tasks, including large-scale multi-modal registration and unsupervised inter-subject brain registration, as well as the first microscopy-focused benchmark within Learn2Reg. The new datasets also inspired new method developments, including invertibility constraints, pyramid features, keypoints alignment and instance optimisation.

Tao Qian, Lei Dai, Liming Zhang et al.

A gradient-free deterministic method is developed to solve global optimization problems for Lipschitz continuous functions defined in arbitrary path-wise connected compact sets in Euclidean spaces. The method can be regarded as granular sieving with synchronous analysis in both the domain and range of the objective function. With straightforward mathematical formulation applicable to both univariate and multivariate objective functions, the global minimum value and all the global minimizers are located through two decreasing sequences of compact sets in, respectively, the domain and range spaces. The algorithm is easy to implement with moderate computational cost. The method is tested against extensive benchmark functions in the literature. The experimental results show remarkable effectiveness and applicability of the algorithm.