# LINN: Lifting Inspired Invertible Neural Network for Image Denoising

arXiv: https://arxiv.org/abs/2105.03303 · HTML: https://mlsanity.com/paper/2105.03303/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 7 May 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [i-RevNet: Deep Invertible Networks](https://mlsanity.com/paper/1802.07088/) (2018)

## Built on by (most cited first, 6 of 6)

- [Imperceptible Adversarial Attack via Invertible Neural Networks](https://mlsanity.com/paper/2211.15030/) (2022)
- [Robust Time Series Denoising with Learnable Wavelet Packet Transform](https://mlsanity.com/paper/2206.06126/) (2022)
- [A Lightweight Deep Exclusion Unfolding Network for Single Image Reflection Removal](https://mlsanity.com/paper/2503.01938/) (2025)
- [SVASTIN: Sparse Video Adversarial Attack via Spatio-Temporal Invertible Neural Networks](https://mlsanity.com/paper/2406.01894/) (2024)
- [SMILENet: Unleashing Extra-Large Capacity Image Steganography via a Synergistic Mosaic InvertibLE Hiding Network](https://mlsanity.com/paper/2503.05118/) (2025)
- [RINS-T: Robust Implicit Neural Solvers for Time Series Linear Inverse Problems](https://mlsanity.com/paper/2510.17396/) (2025)

## Abstract (arXiv)

In this paper, we propose an invertible neural network for image denoising (DnINN) inspired by the transform-based denoising framework. The proposed DnINN consists of an invertible neural network called LINN whose architecture is inspired by the lifting scheme in wavelet theory and a sparsity-driven denoising network which is used to remove noise from the transform coefficients. The denoising operation is performed with a single soft-thresholding operation or with a learned iterative shrinkage thresholding network. The forward pass of LINN produces an over-complete representation which is more suitable for denoising. The denoised image is reconstructed using the backward pass of LINN using the output of the denoising network. The simulation results show that the proposed DnINN method achieves results comparable to the DnCNN method while only requiring 1/4 of learnable parameters.