# Deep Kernel Representation for Image Reconstruction in PET

arXiv: https://arxiv.org/abs/2110.01174 · HTML: https://mlsanity.com/paper/2110.01174/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 4 Oct 2021.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [Iterative PET Image Reconstruction Using Convolutional Neural Network Representation](https://mlsanity.com/paper/1710.03344/) (2017)
- [Direct Reconstruction of Linear Parametric Images from Dynamic PET Using Nonlocal Deep Image Prior](https://mlsanity.com/paper/2106.10359/) (2021)

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

- [Neural KEM: A Kernel Method with Deep Coefficient Prior for PET Image Reconstruction](https://mlsanity.com/paper/2201.01443/) (2022)
- [DULDA: Dual-domain Unsupervised Learned Descent Algorithm for PET image reconstruction](https://mlsanity.com/paper/2303.04661/) (2023)
- [Deep kernel representations of latent space features for low-dose PET-MR imaging robust to variable dose reduction](https://mlsanity.com/paper/2409.06198/) (2024)
- [Dynamic PET Image Reconstruction via Non-negative INR Factorization](https://mlsanity.com/paper/2503.08025/) (2025)
- [Physics-Constrained Diffusion Reconstruction with Posterior Correction for Quantitative and Fast PET Imaging](https://mlsanity.com/paper/2508.14364/) (2025)
- [A Kernel Space-based Multidimensional Sparse Model for Dynamic PET Image Denoising](https://mlsanity.com/paper/2509.18801/) (2025)

## Abstract (arXiv)

Image reconstruction for positron emission tomography (PET) is challenging because of the ill-conditioned tomographic problem and low counting statistics. Kernel methods address this challenge by using kernel representation to incorporate image prior information in the forward model of iterative PET image reconstruction. Existing kernel methods construct the kernels commonly using an empirical process, which may lead to unsatisfactory performance. In this paper, we describe the equivalence between the kernel representation and a trainable neural network model. A deep kernel method is then proposed by exploiting a deep neural network to enable automated learning of an improved kernel model and is directly applicable to single subjects in dynamic PET. The training process utilizes available image prior data to form a set of robust kernels in an optimized way rather than empirically. The results from computer simulations and a real patient dataset demonstrate that the proposed deep kernel method can outperform the existing kernel method and neural network method for dynamic PET image reconstruction.