Dictionary Learning from Incomplete Data
This addresses dictionary learning for incomplete data, which is incremental as it extends an existing algorithm to handle masked data and low-rank components.
The paper tackles dictionary learning from incomplete data by extending the ITKrM algorithm to handle masked training data (ITKrMM) and adapting it for data with low-rank components. Experiments show ITKrMM achieves similar or better reconstruction quality with faster speed compared to counterparts, demonstrated in image inpainting.
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.