Implicit Neural Representations with Fourier Kolmogorov-Arnold Networks
Authors: name: Ali Mehrabian, name: Parsa Mojarad Adi, name: Moein Heidari, name: Ilker Hacihaliloglu

Implicit neural representations (INRs) use neural networks to provide
continuous and resolution-independent representations of complex signals with a
small number of parameters. However, existing INR models often fail to capture
important frequency components specific to each task. To address this issue, in
this paper, we propose a Fourier Kolmogorov Arnold network (FKAN) for INRs. The
proposed FKAN utilizes learnable activation functions modeled as Fourier series
in the first layer to effectively control and learn the task-specific frequency
components. In addition, the activation functions with learnable Fourier
coefficients improve the ability of the network to capture complex patterns and
details, which is beneficial for high-resolution and high-dimensional data.
Experimental results show that our proposed FKAN model outperforms three
state-of-the-art baseline schemes, and improves the peak signal-to-noise ratio
(PSNR) and structural similarity index measure (SSIM) for the image
representation task and intersection over union (IoU) for the 3D occupancy
volume representation task, respectively.