# One-Dimensional Deep Image Prior for Curve Fitting of S-Parameters from Electromagnetic Solvers

arXiv: https://arxiv.org/abs/2306.04001 · HTML: https://mlsanity.com/paper/2306.04001/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 6 Jun 2023.

## Builds on (most cited first, 6 of 6)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [A Bayesian Perspective on the Deep Image Prior](https://mlsanity.com/paper/1904.07457/) (2019)
- [Uncertainty Estimation in Medical Image Denoising with Bayesian Deep Image Prior](https://mlsanity.com/paper/2008.08837/) (2020)
- [Uncertainty Estimation for Computed Tomography with a Linearised Deep Image Prior](https://mlsanity.com/paper/2203.00479/) (2022)
- [One-dimensional Deep Image Prior for Time Series Inverse Problems](https://mlsanity.com/paper/1904.08594/) (2019)

## Built on by (most cited first, 1 of 1)

- [Efficient RF Passive Components Modeling with Bayesian Online Learning and Uncertainty Aware Sampling](https://mlsanity.com/paper/2511.15125/) (2025)

## Abstract (arXiv)

A key problem when modeling signal integrity for passive filters and interconnects in IC packages is the need for multiple S-parameter measurements within a desired frequency band to obtain adequate resolution. These samples are often computationally expensive to obtain using electromagnetic (EM) field solvers. Therefore, a common approach is to select a small subset of the necessary samples and use an appropriate fitting mechanism to recreate a densely-sampled broadband representation. We present the first deep generative model-based approach to fit S-parameters from EM solvers using one-dimensional Deep Image Prior (DIP). DIP is a technique that optimizes the weights of a randomly-initialized convolutional neural network to fit a signal from noisy or under-determined measurements. We design a custom architecture and propose a novel regularization inspired by smoothing splines that penalizes discontinuous jumps. We experimentally compare DIP to publicly available and proprietary industrial implementations of Vector Fitting (VF), the industry-standard tool for fitting S-parameters. Relative to publicly available implementations of VF, our method shows superior performance on nearly all test examples using only 5-15% of the frequency samples. Our method is also competitive to proprietary VF tools and often outperforms them for challenging input instances.