Accelerating GMM-Based Patch Priors for Image Restoration: Three Ingredients for a Speed-Up

Area of Science:

• Computer Vision
• Image Processing
• Machine Learning

Background:

• Image restoration aims to recover clean images from degraded observations.
• The Expected Patch Log-Likelihood (EPLL) algorithm, using Gaussian Mixture Models (GMMs), is effective but computationally expensive.
• High runtime complexity limits the practical application of EPLL.

Purpose of the Study:

• To develop a significantly faster version of the EPLL algorithm for practical image restoration.
• To maintain high restored image quality while drastically reducing computation time.
• To demonstrate the algorithm's effectiveness across diverse image restoration tasks.

Main Methods:

• Proposed three approximations to the original EPLL algorithm.
• Developed the Fast EPLL (FEPLL) algorithm.
• Evaluated FEPLL on various inverse problems including denoising, deblurring, super-resolution, inpainting, and devignetting.

Main Results:

• Achieved a two-order magnitude speed-up compared to the original EPLL algorithm.
• Restored image quality degradation was negligible (less than 0.5 dB).
• FEPLL restored images in under 0.5 seconds for all tested degradations without specialized optimizations.

Conclusions:

• The FEPLL algorithm offers a practical and efficient solution for image restoration.
• FEPLL provides a significant speed improvement over EPLL with minimal loss in image quality.
• This is the first algorithm capable of competitive pixel image restoration across multiple degradations within seconds.