# Exact Sparse Orthogonal Dictionary Learning

arXiv: https://arxiv.org/abs/2103.09085 · HTML: https://mlsanity.com/paper/2103.09085/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 47 references that are in the map.
- First posted on arXiv 14 Mar 2021.

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

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning](https://mlsanity.com/paper/1708.01955/) (2017)
- [Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1811.05642/) (2018)
- [Efficient Dictionary Learning with Gradient Descent](https://mlsanity.com/paper/1809.10313/) (2018)
- [Spherical Principal Component Analysis](https://mlsanity.com/paper/1903.06877/) (2019)
- [An Extension of Fast Iterative Shrinkage-thresholding to Riemannian Optimization for Sparse Principal Component Analysis](https://mlsanity.com/paper/1909.05485/) (2019)
- [Geometry of Factored Nuclear Norm Regularization](https://mlsanity.com/paper/1704.01265/) (2017)

## Abstract (arXiv)

Over the past decade, learning a dictionary from input images for sparse modeling has been one of the topics which receive most research attention in image processing and compressed sensing. Most existing dictionary learning methods consider an over-complete dictionary, such as the K-SVD method, which may result in high mutual incoherence and therefore has a negative impact in recognition. On the other side, the sparse codes are usually optimized by adding the ℓ0 or ℓ1-norm penalty, but with no strict sparsity guarantee. In this paper, we propose an orthogonal dictionary learning model which can obtain strictly sparse codes and orthogonal dictionary with global sequence convergence guarantee. We find that our method can result in better denoising results than over-complete dictionary based learning methods, and has the additional advantage of high computation efficiency.