Image Restoration

Image Restoration in Computer Vision

Introduction

The primary goal of image restoration is to recover an “ideal” image from a degraded version. This process attempts to reverse the effects of imperfections introduced during image acquisition or transmission.

Key Concepts

Inverse Filtering (Idealized)

The fundamental concept can be represented by the following equation:

$\text{Ideal Image}=(\text{DM}{)}^{-1}\ast \text{Restored Image}$

Where:

• Ideal Image: The original, uncorrupted image (what we want).
• Restored Image: The image after applying a restoration technique (our best estimate).
• DM: Degradation Model (also called Degradation Function or Point Spread Function - PSF).
• (DM)⁻¹: Inverse of the Degradation Model.

Degradation Model (DM)

• The DM mathematically describes how the image was degraded.
• It models the blurring, noise, or geometric distortions that affected the original image.

Common Types of Degradation:

• Blur:
  • Motion blur (camera or subject movement).
  • Out-of-focus blur (lens not properly focused).
  • Atmospheric turbulence (for aerial or astronomical images).
• Noise:
  • Random variations in pixel values.
  • Often introduced by image sensors (sensor noise) or during transmission (transmission errors).
• Geometric Distortions:
  • Warping, twisting, or other spatial transformations of the image.