Implicit Neural Representations (INRs) are continuous function learners for conventional digital signal representations. With the aid of positional embeddings and/or exhaustively fine-tuned activation functions, INRs have surpassed many limitations of traditional discrete representations. However, existing works only find a continuous representation for the digital signal by solely using a single, fixed activation function throughout the INR, and it has not yet been explored to match the INR to the given signal. As current INRs are not matched to the signal being represented by the INR, we hypothesize that this approach could restrict the representation power and generalization capabilities of INRs, limiting their broader applicability. A way to match the INR to the signal being represented is through matching the activation of each layer in the sense of minimizing the mean squared loss. In this paper, we introduce MIRE, a method to find the highly matched activation function for each layer in INR through dictionary learning. To showcase the effectiveness of the proposed method, we utilize a dictionary that includes seven activation atoms: Raised Cosines (RC), Root Raised Cosines (RRC), Prolate Spheroidal Wave Function (PSWF), Sinc, Gabor Wavelet, Gaussian, and Sinusoidal. Experimental results demonstrate that MIRE not only significantly improves INR performance across various tasks, such as image representation, image inpainting, 3D shape representation, novel view synthesis, super-resolution, and reliable edge detection, but also eliminates the need for the previously required exhaustive search for activation parameters, which had to be conducted even before INR training could begin.

Implicit Neural Representations (INRs) are increasingly recognized as a versatile data modality for representing discretized signals, offering benefits such as infinite query resolution and reduced storage requirements. Existing signal compression approaches for INRs typically employ one of two strategies: 1. direct quantization with entropy coding of the trained INR; 2. deriving a latent code on top of the INR through a learnable transformation. Thus, their performance is heavily dependent on the quantization and entropy coding schemes employed. In this paper, we introduce SINR, an innovative compression algorithm that leverages the patterns in the vector spaces formed by weights of INRs. We compress these vector spaces using a high-dimensional sparse code within a dictionary. Further analysis reveals that the atoms of the dictionary used to generate the sparse code do not need to be learned or transmitted to successfully recover the INR weights. We demonstrate that the proposed approach can be integrated with any existing INR-based signal compression technique. Our results indicate that SINR achieves substantial reductions in storage requirements for INRs across various configurations, outperforming conventional INR-based compression baselines. Furthermore, SINR maintains high-quality decoding across diverse data modalities, including images, occupancy fields, and Neural Radiance Fields.

Implicit Neural Representations (INRs) provide a continuous mapping between the coordinates of a signal and the corresponding values. As the performance of INRs heavily depends on the choice of nonlinear-activation functions, there has been a significant focus on encoding explicit signals within INRs using diverse activation functions. Despite recent advancements, existing INRs often encounter significant challenges, particularly at fine scales where they often introduce noise-like artifacts over smoother areas compromising the quality of the output. Moreover, they frequently struggle to generalize to unseen coordinates. These drawbacks highlight a critical area for further research and development to enhance the robustness and applicability of INRs across diverse scenarios. To address this challenge, we introduce the Prolate Spheroidal Wave Function-based Implicit Neural Representations (PIN), which exploits the optimal space-frequency domain concentration of Prolate Spheroidal Wave Functions (PSWFs) as the nonlinear mechanism in INRs. Our experimental results reveal that PIN excels not only in representing images and 3D shapes but also significantly outperforms existing methods in various vision tasks that require INR generalization, including image inpainting, novel view synthesis, edge detection, and image denoising.