# Spectral2Spectral: Image-spectral Similarity Assisted Spectral CT Deep Reconstruction without Reference

arXiv: https://arxiv.org/abs/2210.01125 · HTML: https://mlsanity.com/paper/2210.01125/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 58 references that are in the map.
- First posted on arXiv 3 Oct 2022.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Low-Dose CT with a Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)](https://mlsanity.com/paper/1702.00288/) (2017)
- [Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images](https://mlsanity.com/paper/2101.02824/) (2021)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction](https://mlsanity.com/paper/1610.09736/) (2016)
- [Momentum-Net: Fast and convergent iterative neural network for inverse problems](https://mlsanity.com/paper/1907.11818/) (2019)
- [Radon Inversion via Deep Learning](https://mlsanity.com/paper/1808.03015/) (2018)
- [Quadratic Autoencoder (Q-AE) for Low-dose CT Denoising](https://mlsanity.com/paper/1901.05593/) (2019)
- [Low-dose CT denoising with convolutional neural network](https://mlsanity.com/paper/1610.00321/) (2016)
- [Deep BCD-Net Using Identical Encoding-Decoding CNN Structures for Iterative Image Recovery](https://mlsanity.com/paper/1802.07129/) (2018)
- [Low-dose spectral CT reconstruction using L0 image gradient and tensor dictionary](https://mlsanity.com/paper/1801.01452/) (2017)
- [Deep Learning based Spectral CT Imaging](https://mlsanity.com/paper/2008.13570/) (2020)
- [Attention-embedded Quadratic Network (Qttention) for Effective and Interpretable Bearing Fault Diagnosis](https://mlsanity.com/paper/2206.00390/) (2022)
- [Synergistic Multi-spectral CT Reconstruction with Directional Total Variation](https://mlsanity.com/paper/2101.01834/) (2021)
- [Fourth-Order Nonlocal Tensor Decomposition Model for Spectral Computed Tomography](https://mlsanity.com/paper/2010.14361/) (2020)

## Built on by (most cited first, 5 of 5)

- [Two-and-a-half Order Score-based Model for Solving 3D Ill-posed Inverse Problems](https://mlsanity.com/paper/2308.08511/) (2023)
- [PWD: Prior-Guided and Wavelet-Enhanced Diffusion Model for Limited-Angle CT](https://mlsanity.com/paper/2507.05317/) (2025)
- [Cross-Distribution Diffusion Priors-Driven Iterative Reconstruction for Sparse-View CT](https://mlsanity.com/paper/2509.13576/) (2025)
- [AS-Mamba: Asymmetric Self-Guided Mamba Decoupled Iterative Network for Metal Artifact Reduction](https://mlsanity.com/paper/2602.06350/) (2026)
- [SCOUT: Fast Spectral CT Imaging in Ultra LOw-data Regimes via PseUdo-label GeneraTion](https://mlsanity.com/paper/2603.00687/) (2026)

## Abstract (arXiv)

Spectral computed tomography based on a photon-counting detector (PCD) attracts more and more attentions since it has the capability to provide more accurate identification and quantitative analysis for biomedical materials. The limited number of photons within narrow energy bins leads to imaging results of low signal-noise ratio. The existing supervised deep reconstruction networks for CT reconstruction are difficult to address these challenges because it is usually impossible to acquire noise-free clinical images with clear structures as references. In this paper, we propose an iterative deep reconstruction network to synergize unsupervised method and data priors into a unified framework, named as Spectral2Spectral. Our Spectral2Spectral employs an unsupervised deep training strategy to obtain high-quality images from noisy data in an end-to-end fashion. The structural similarity prior within image-spectral domain is refined as a regularization term to further constrain the network training. The weights of neural network are automatically updated to capture image features and structures within the iterative process. Three large-scale preclinical datasets experiments demonstrate that the Spectral2spectral reconstructs better image quality than other the state-of-the-art methods.