NASA-INR: Non-linear Adaptive Spectrally-spanning Activation for Implicit Neural Representation

Implicit neural representations (INRs) have emerged as a powerful approach to model complex data offering continuous, resolution independent, and differentiable representations. However, existing methods do not explicitly address symmetry induced spectral attenuation without relying on complex modulation. To counteract this effect, we introduce a non-linear adaptive spectral spanning activation(NASA). We also introduce a non-linear phase expansion (NOPE) for activations in INR. Using harmonic analysis and Chebyshev polynomials, we showcase that the resulting activations contain both odd and even polynomial components, leading to a reduced spectral attenuation in the activation. We test where NASA stands among other existing activations. Furthermore, we investigate how the addition of NOPE to existing activations and adaptive forms of existing activations with tunable parameters compare with their non-modified forms. Finally, the resulting models are further evaluated on image reconstruction, inpainting, super-resolution, and denoising tasks against their classic counterparts. Through our work, nearest SOTA methods were surpassed by a mean increment of 2.57 dB in image reconstruction, 0.61 dB in super resolution, 0.26 dB in image inpainting 0.26. Overall, the study investigates phase asymmetry as a possible design dimension for improving the spectral representation capabilities of implicit neural networks.