Fast dictionary learning from incomplete data

Area of Science:

• Machine Learning
• Signal Processing
• Computer Vision

Background:

• Dictionary learning is crucial for signal processing and machine learning.
• Existing methods struggle with incomplete or masked training data.
• Low-rank components in data can significantly impact learning performance.

Purpose of the Study:

• To extend the iterative thresholding and K residual means (ITKrM) algorithm for learning dictionaries from incomplete data (ITKrMM).
• To adapt the algorithm for data with a low-rank component and recover this component from incomplete data.
• To evaluate the performance of the proposed algorithm against existing methods in synthetic and real-world image data.

Main Methods:

• Extension of the ITKrM algorithm to handle masked training data (ITKrMM).
• Adaptation of the algorithm to incorporate and recover low-rank data components.
• Comparative analysis using synthetic data and image datasets, including application to image inpainting.

Main Results:

• ITKrMM effectively learns dictionaries from incomplete data, outperforming counterparts when a low-rank component is present.
• The algorithm demonstrates favorable computational complexity and consistency compared to wKSVD and BPFA.
• In sparsity-based image inpainting, ITKrMM dictionaries achieve competitive or superior performance over pre-defined dictionary methods.

Conclusions:

• The proposed ITKrMM algorithm offers a robust solution for dictionary learning with incomplete data, especially when low-rank structures are present.
• Incorporating corruption information and low-rank component recovery enhances dictionary learning accuracy and applicability.
• The learned dictionaries are effective for image inpainting, showing the practical utility of the developed method.