# Quadratic Autoencoder (Q-AE) for Low-dose CT Denoising

arXiv: https://arxiv.org/abs/1901.05593 · HTML: https://mlsanity.com/paper/1901.05593/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2019.

## Built on by (most cited first, 30 of 35)

- [DU-GAN: Generative Adversarial Networks with Dual-Domain U-Net Based Discriminators for Low-Dose CT Denoising](https://mlsanity.com/paper/2108.10772/) (2021)
- [CTformer: Convolution-free Token2Token Dilated Vision Transformer for Low-dose CT Denoising](https://mlsanity.com/paper/2202.13517/) (2022)
- [TED-net: Convolution-free T2T Vision Transformer-based Encoder-decoder Dilation network for Low-dose CT Denoising](https://mlsanity.com/paper/2106.04650/) (2021)
- [On Expressivity and Trainability of Quadratic Networks](https://mlsanity.com/paper/2110.06081/) (2021)
- [DenoMamba: A fused state-space model for low-dose CT denoising](https://mlsanity.com/paper/2409.13094/) (2024)
- [Spatially Covariant Lesion Segmentation](https://mlsanity.com/paper/2301.07895/) (2023)
- [Ultra Low-Parameter Denoising: Trainable Bilateral Filter Layers in Computed Tomography](https://mlsanity.com/paper/2201.10345/) (2022)
- [Towards NeuroAI: Introducing Neuronal Diversity into Artificial Neural Networks](https://mlsanity.com/paper/2301.09245/) (2023)
- [One Neuron Saved Is One Neuron Earned: On Parametric Efficiency of Quadratic Networks](https://mlsanity.com/paper/2303.06316/) (2023)
- [Quadratic Neuron-empowered Heterogeneous Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2204.01707/) (2022)
- [Trainable Joint Bilateral Filters for Enhanced Prediction Stability in Low-dose CT](https://mlsanity.com/paper/2207.07368/) (2022)
- [Spectral2Spectral: Image-spectral Similarity Assisted Spectral CT Deep Reconstruction without Reference](https://mlsanity.com/paper/2210.01125/) (2022)
- [Masked Autoencoders for Low dose CT denoising](https://mlsanity.com/paper/2210.04944/) (2022)
- [Unsupervised Domain Adaptation for Low-dose CT Reconstruction via Bayesian Uncertainty Alignment](https://mlsanity.com/paper/2302.13251/) (2023)
- [Generative Models Improve Radiomics Reproducibility in Low Dose CTs: A Simulation Study](https://mlsanity.com/paper/2104.15050/) (2021)
- [Supervision by Denoising for Medical Image Segmentation](https://mlsanity.com/paper/2202.02952/) (2022)
- [Limited Parameter Denoising for Low-dose X-ray Computed Tomography Using Deep Reinforcement Learning](https://mlsanity.com/paper/2203.14794/) (2022)
- [No One-Size-Fits-All Neurons: Task-based Neurons for Artificial Neural Networks](https://mlsanity.com/paper/2405.02369/) (2024)
- [Second-Order Component Analysis for Fault Detection](https://mlsanity.com/paper/2103.07303/) (2021)
- [Two-stage Deep Denoising with Self-guided Noise Attention for Multimodal Medical Images](https://mlsanity.com/paper/2503.06827/) (2025)
- [SQ-Swin: a Pretrained Siamese Quadratic Swin Transformer for Lettuce Browning Prediction](https://mlsanity.com/paper/2209.07683/) (2022)
- [Cross-domain Denoising for Low-dose Multi-frame Spiral Computed Tomography](https://mlsanity.com/paper/2304.10839/) (2023)
- [Cloud-RAIN: Point Cloud Analysis with Reflectional Invariance](https://mlsanity.com/paper/2305.07814/) (2023)
- [Enhanced Low-Dose CT Image Reconstruction by Domain and Task Shifting Gaussian Denoisers](https://mlsanity.com/paper/2403.03551/) (2024)
- [MAN: Latent Diffusion Enhanced Multistage Anti-Noise Network for Efficient and High-Quality Low-Dose CT Image Denoising](https://mlsanity.com/paper/2509.23603/) (2025)
- [Low Dose Helical CBCT denoising by using domain filtering with deep reinforcement learning](https://mlsanity.com/paper/2104.00889/) (2021)
- [GCN-MIF: Graph Convolutional Network with Multi-Information Fusion for Low-dose CT Denoising](https://mlsanity.com/paper/2105.07146/) (2021)
- [Image Denoising via Style Disentanglement](https://mlsanity.com/paper/2309.14755/) (2023)
- [LoMAE: Low-level Vision Masked Autoencoders for Low-dose CT Denoising](https://mlsanity.com/paper/2310.12405/) (2023)
- [Retinal Vessel Segmentation via Neuron Programming](https://mlsanity.com/paper/2411.11110/) (2024)

## Abstract (arXiv)

Inspired by complexity and diversity of biological neurons, our group proposed quadratic neurons by replacing the inner product in current artificial neurons with a quadratic operation on input data, thereby enhancing the capability of an individual neuron. Along this direction, we are motivated to evaluate the power of quadratic neurons in popular network architectures, simulating human-like learning in the form of quadratic-neuron-based deep learning. Our prior theoretical studies have shown important merits of quadratic neurons and networks in representation, efficiency, and interpretability. In this paper, we use quadratic neurons to construct an encoder-decoder structure, referred as the quadratic autoencoder, and apply it to low-dose CT denoising. The experimental results on the Mayo low-dose CT dataset demonstrate the utility of quadratic autoencoder in terms of image denoising and model efficiency. To our best knowledge, this is the first time that the deep learning approach is implemented with a new type of neurons and demonstrates a significant potential in the medical imaging field.