Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems

Area of Science:

• Signal Processing
• Machine Learning
• Computer Vision

Background:

• Sparsity in transform domains is key for compression, denoising, and inverse problems.
• Data-driven synthesis dictionaries offer advantages over analytical models.
• Dictionary learning is computationally challenging due to non-convexity and NP-hard sparse coding.

Purpose of the Study:

• To develop efficient algorithms for aggregate sparsity penalized dictionary learning.
• To propose novel methods for dictionary-blind image reconstruction.
• To analyze the convergence and performance of the developed algorithms.

Main Methods:

• Approximating data as a sum of sparse rank-one matrices.
• Employing block coordinate descent for unknown estimation.
• Developing closed-form solutions for dictionary learning and image reconstruction.

Main Results:

• The proposed block coordinate descent algorithms yield efficient closed-form solutions.
• Novel algorithms for dictionary-blind image reconstruction demonstrate effectiveness.
• Numerical experiments confirm promising performance and speedups over existing methods.

Conclusions:

• The developed methods provide efficient solutions for sparse data representation and compressed sensing-based image reconstruction.
• The aggregate sparsity and block coordinate descent approach enhances computational efficiency.
• The study contributes significant advancements in dictionary learning and adaptive image reconstruction.