Implicit Neural Representations: A Signal Processing Perspective

Implicit Neural Representations (INRs) have been proven successful in encoding continuous signals through coordinate-based networks, yet facing a spectral dilemma: periodic activations capture fine details but act as all-pass filters that memorise noise, while spatially compact activations regularise effectively but suffer from low-frequency bias. Existing attempts to resolve this trade-off introduce computational overhead or tuning frailty. We propose to model each neuron's activation as the steady-state response of a sinusoidally-forced damped harmonic oscillator, whose amplitude naturally governs the network's spectral selectivity during training. By jointly optimising the oscillator parameters alongside the network weights, our method adapts to the target signal's spectral content without explicit regularisation. Initialised in the stopband, the network exhibits a coarse-to-fine learning curriculum that progressively expands its spectral gate, capturing low-frequency structures first and high-frequency details only when justified by the reconstruction objective. Comprehensive experiments show that our approach consistently achieves state-of-the-art or competitive results against established INRs, while requiring no task-specific tuning of any hyperparameters.

Implicit Neural Representations (INRs) parameterized by multilayer perceptrons excel at modeling continuous signals. However, a key challenge persists as INRs fundamentally suffer from spectral bias and information cross-talk. When a single network attempts to capture multi-scale phenomena, high-frequency weight updates destructively interfere with the underlying low-frequency structural approximation. We introduce Scale and Learn INR (ScaLe-INR), a novel multi-branch architecture that resolves these limitations by explicitly matching the signal's frequency spectrum with the optimal operating region of the INR. Drawing upon the Fourier inverse scaling theorem we demonstrate that applying directional coordinate scaling expands a network's representational bandwidth along specific spatial axes. To mathematically enforce functional disentanglement and minimize task-specific information leakage between branches, we propose a Directional Edge Guidance Loss, a spatially-conditioned sparsity prior derived from ground-truth gradients. By constraining the high-frequency branches to act as strict, localized edge-filters, ScaLe-INR eliminates spectral cross-talk, accelerates convergence, and achieves high-fidelity signal reconstruction on complex multi-scale topologies. We evaluate ScaLe-INR across diverse reconstruction and inverse tasks, demonstrating substantial performance gains over existing state-of-the-art (SOTA) methods. The proposed architecture improves upon the nearest baselines by +5.16 dB in image reconstruction and +0.65 dB in image denoising. Furthermore, it achieve an impressive figure of 50.02 dB on audio reconstruction and 0.999 IOU(Intersection Over Union) on 3D reconstruction which beats the all SOTA models.

Implicit neural representation (INR) has emerged as a powerful prior for multi-dimensional data (e.g., multispectral images and videos). However, most INR methods employing periodic activation functions (e.g., Sine) predominantly rely on function composition. This mechanism introduces optimization instability as network depth increases, thereby limiting their performance. Meanwhile, these methods fail to incorporate proper physical priors to effectively alleviate spectrum bias. To address these issues, inspired by the commonalities between deep periodic networks and generalized Fourier series, we propose a novel Calibrated Harmonic Overlaid Implicit Neural Representation (CHOIR). Specifically, we utilize Coordinated Harmonic Superposition (CHS) to replace the conventional function composition used in most INRs, thereby ensuring optimization stability when scaling network depth. Furthermore, we introduce a Perceptual Spectrum Calibration (PSC) to mitigate spectrum bias. This calibration embeds the ubiquitous power-law spectrum prior of natural images and adjusts the globally fixed spectrum towards a physically plausible log-uniform distribution. Extensive experiments on various multidimensional data recovery problems demonstrate that our method achieves superior performance over state-of-the-art approaches. Code is available at https://github.com/chorl0229/CHOIR.