# Dictionary Learning from Incomplete Data

## TL;DR

This paper introduces ITKrMM, an extension of the ITKrM algorithm, for dictionary learning from incomplete data, including low-rank components, with applications in image inpainting demonstrating improved speed and comparable quality.

## Contribution

It develops a novel algorithm for dictionary learning from incomplete data, incorporating low-rank recovery and demonstrating superior performance in image inpainting tasks.

## Key findings

- ITKrMM effectively learns dictionaries from incomplete data.
- Incorporating corruption information improves learning performance.
- ITKrMM outperforms similar methods in speed with comparable quality.

## Abstract

This paper extends the recently proposed and theoretically justified iterative thresholding and $K$ residual means algorithm ITKrM to learning dicionaries from incomplete/masked training data (ITKrMM). It further adapts the algorithm to the presence of a low rank component in the data and provides a strategy for recovering this low rank component again from incomplete data. Several synthetic experiments show the advantages of incorporating information about the corruption into the algorithm. Finally, image inpainting is considered as application example, which demonstrates the superior performance of ITKrMM in terms of speed at similar or better reconstruction quality compared to its closest dictionary learning counterpart.