# Deep learning based dictionary learning and tomographic image reconstruction

arXiv: https://arxiv.org/abs/2108.11730 · HTML: https://mlsanity.com/paper/2108.11730/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 88 references that are in the map.
- First posted on arXiv 26 Aug 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning](https://mlsanity.com/paper/1904.02816/) (2019)
- [Computed Tomography Reconstruction Using Deep Image Prior and Learned Reconstruction Methods](https://mlsanity.com/paper/2003.04989/) (2020)
- [Total Deep Variation for Linear Inverse Problems](https://mlsanity.com/paper/2001.05005/) (2020)
- [Convolutional Neural Networks Analyzed via Convolutional Sparse Coding](https://mlsanity.com/paper/1607.08194/) (2016)
- [New Algorithms for Learning Incoherent and Overcomplete Dictionaries](https://mlsanity.com/paper/1308.6273/) (2013)
- [On Multi-Layer Basis Pursuit, Efficient Algorithms and Convolutional Neural Networks](https://mlsanity.com/paper/1806.00701/) (2018)
- [Rethinking the CSC Model for Natural Images](https://mlsanity.com/paper/1909.05742/) (2019)
- [Convolutional Sparse Coding for Compressed Sensing CT Reconstruction](https://mlsanity.com/paper/1903.08549/) (2019)
- [On the Computational Intractability of Exact and Approximate Dictionary Learning](https://mlsanity.com/paper/1405.6664/) (2014)
- [Multi-Layer Convolutional Sparse Modeling: Pursuit and Dictionary Learning](https://mlsanity.com/paper/1708.08705/) (2017)
- [Deep Dictionary Learning: A PARametric NETwork Approach](https://mlsanity.com/paper/1803.04022/) (2018)
- [Accelerated Forward-Backward Optimization using Deep Learning](https://mlsanity.com/paper/2105.05210/) (2021)
- [Deep synthesis regularization of inverse problems](https://mlsanity.com/paper/2002.00155/) (2020)
- [Computationally Efficient Deep Neural Network for Computed Tomography Image Reconstruction](https://mlsanity.com/paper/1810.03999/) (2018)
- [A convex variational model for learning convolutional image atoms from incomplete data](https://mlsanity.com/paper/1812.03077/) (2018)

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

- [Deep Learning for Material Decomposition in Photon-Counting CT](https://mlsanity.com/paper/2208.03360/) (2022)

## Abstract (arXiv)

This work presents an approach for image reconstruction in clinical low-dose tomography that combines principles from sparse signal processing with ideas from deep learning. First, we describe sparse signal representation in terms of dictionaries from a statistical perspective and interpret dictionary learning as a process of aligning distribution that arises from a generative model with empirical distribution of true signals. As a result we can see that sparse coding with learned dictionaries resembles a specific variational autoencoder, where the decoder is a linear function and the encoder is a sparse coding algorithm. Next, we show that dictionary learning can also benefit from computational advancements introduced in the context of deep learning, such as parallelism and as stochastic optimization. Finally, we show that regularization by dictionaries achieves competitive performance in computed tomography (CT) reconstruction comparing to state-of-the-art model based and data driven approaches.