Adaptive method for selecting basis functions in Kolmogorov–Arnold networks for magnetic resonance image enhancement

A way to improve the quality of magnetic resonance image processing using the Kolmogorov–Arnold networks for deep feature filtering in the convolutional neural network is studied. Recently proposed Kolmogorov–Arnold networks are inspired by the representation theorem of the same name from real analysis and approximation theory. It states that every multivariate continuous function on a compact set can be represented as a superposition of continuous single-variable functions. However, further gradient descent application imposes restrictions on the inner Kolmogorov functions to be at least differentiable, that’s why, in practice, they are searched in a linear span of B-Splines or some other differentiable basis functions. In this study we propose an adaptive method of basis functions selection by the model itself during training, mitigating the rule of thumb choice of that basis functions. The method is based on the attention mechanism, successfully used in state-of-the-art transformers. The proposed approach is tested on magnetic resonance images enhancement on IXI dataset and demonstrates the best average PSNR and TV over the synthetic testing dataset. Without loss of generality, the system of basis functions included: B-splines, Chebyshev polynomials and Hermite functions.

Kolmogorov–Arnold networks, Attention mechanism, Chebyshev polynomials, Hermite functions, Gibbs phenomenon, Magnetic resonance imaging