An Algorithm for Learning Orthonormal Matrix Codebooks for Adaptive Transform Coding.

Area of Science:

• Signal Processing
• Data Compression
• Machine Learning

Background:

• Adaptive transform coding is crucial for efficient data compression.
• Designing optimal orthonormal transform matrices for non-stationary data is challenging.
• Existing methods often struggle with the orthonormality constraint.

Purpose of the Study:

• To propose a novel data-driven approach for designing orthonormal transform matrices.
• To minimize the mean square error (MSE) in adaptive transform coding.
• To address the challenge of imposing orthonormality constraints during optimization.

Main Methods:

• Utilizing block-coordinate descent algorithms.
• Employing simple probability models (Gaussian, Laplacian) for transform coefficients.
• Mapping the constrained optimization problem to an unconstrained problem on the Stiefel manifold.
• Leveraging manifold optimization algorithms.

Main Results:

• Successfully designed orthonormal transform matrices for adaptive transform coding.
• Demonstrated effectiveness on still images and video prediction residuals.
• Achieved competitive or superior performance compared to other content-adaptive transforms.
• Proposed an extension for separable transforms.

Conclusions:

• The proposed data-driven method effectively designs orthonormal transform matrices for adaptive transform coding.
• The manifold optimization approach successfully handles the orthonormality constraint.
• The method shows promise for improving compression efficiency in image and video coding.