Convolutional Analysis Operator Learning: Acceleration and Convergence | JoVE Visualize

Area of Science:

Signal Processing
Computer Vision
Machine Learning
Image Reconstruction

Background:

Kernel learning in signal processing and computer vision often uses patch-domain methods, which are memory-intensive for large datasets and complex models.
Existing synthesis-based convolutional dictionary learning methods address memory issues but are limited in scope.
There is a need for efficient and memory-conscious methods for learning convolutional operators, especially for high-dimensional signal recovery.

Purpose of the Study:

To propose a novel Convolutional Analysis Operator Learning (CAOL) framework.
To develop a new convergent Block Proximal Extrapolated Gradient method using a Majorizer (BPEG-M) for solving associated non-convex problems.
To enhance filter diversity and learning efficiency within the CAOL framework.

Main Methods:

Developed a CAOL framework leveraging the convolution perspective for learning analysis sparsifying regularizers.
Introduced a Block Proximal Extrapolated Gradient method using a Majorizer (BPEG-M) for efficient optimization.
Incorporated an orthogonality constraint for tight-frame filter conditions and a diversity regularizer for filter variety.

Main Results:

The BPEG-M method significantly accelerated convergence rates compared to the state-of-the-art Block Proximal Gradient (BPG) method, especially with sharp majorizers.
A convolutional sparsifying regularizer learned via CAOL demonstrated substantial improvements in reconstruction quality for sparse-view computational tomography.
Using more and wider kernels in the learned regularizer effectively preserved edges in reconstructed images.

Conclusions:

The proposed CAOL framework and BPEG-M optimization method offer an efficient and memory-conscious alternative for convolutional operator learning.
The learned regularizers significantly enhance image reconstruction quality, particularly in challenging scenarios like sparse-view CT.
The framework's ability to learn diverse and effective filters opens new avenues for advanced signal processing and computer vision tasks.