Image Restoration



Image Restoration 

Image Restoration is a scientific and mathematical process used to recover an image that has been damaged due to blur, noise, motion, or system errors. The main aim is not beauty, but truth — to get as close as possible to the original image.

Image Restoration

Enhancement vs Restoration

AspectImage EnhancementImage Restoration
FocusVisual improvementAccuracy & recovery
Based onHuman perceptionMathematical models
ExampleIncrease brightnessRemove motion blur

Real-Life Example

  • Enhancement: Instagram filter
  • Restoration: Police restoring CCTV footage for evidence

Image Degradation Model

Why Do Images Get Degraded?

Images get degraded due to:

  • Camera shake
  • Out-of-focus lens
  • Poor lighting
  • Transmission errors
  • Dust, rain, fog

Mathematical Model

g(x, y) = f(x, y) ⊗ h(x, y) + η(x, y)

Meaning of Each Term

TermDetailed Meaning
f(x, y)Perfect original scene
h(x, y)How camera/system distorts image
η(x, y)Random noise (unwanted data)
g(x, y)Final observed image

Simple Analogy

Imagine taking a photo through a dirty glass window:

  • Scene = original image
  • Dirty glass = degradation function
  • Dust & scratches = noise
  • Captured photo = degraded image

Properties of Image Restoration

Key Characteristics

PropertyDetailed Explanation
Model-basedUses known degradation models
DeterministicTries to reverse damage logically
Noise-awareDepends heavily on noise type
ObjectiveMinimum error reconstruction

Important Exam Point: Restoration assumes prior knowledge of degradation.

Noise Models 

Noise is any unwanted disturbance that hides or distorts useful information in an image.

Real-Life Sources of Noise

  • Heat inside camera sensor
  • Low-light photography
  • Wireless image transmission
  • Old scanners

Types of Noise 

NoiseDescriptionReal Example
GaussianRandom variationSmartphone night photo
Salt & PepperBlack & white dotsFax images
PoissonPhoton-based noiseMedical scans
SpeckleMultiplicative noiseUltrasound images

Mean Filters

Mean filter replaces each pixel with the average of surrounding pixels. It smoothens variations.

Real-Life Example: Like averaging opinions in a group — extreme values get neutralized.

Types of Mean Filters

FilterExplanation
ArithmeticSimple average
GeometricReduces Gaussian noise
HarmonicRemoves salt noise
Contra-harmonicRemoves salt or pepper

Disadvantage: Loss of sharp edges

Order Statistics Filters 

Instead of averaging, these filters sort pixel values.

Median Filter 

FeatureExplanation
Uses middle valueIgnores extreme noise
Edge preservingDoes not blur boundaries

Example: Removing white dots from scanned certificates.

Adaptive Filters

Why Adaptive?

Images are not uniform everywhere. Adaptive filters adjust themselves.

Behavior

  • Flat area → more smoothing
  • Edge area → less smoothing

Comparison

AspectNormal FilterAdaptive Filter
Fixed windowYesNo
IntelligentNoYes

Example: Mobile camera AI noise reduction.

Band Reject Filters 

Removes specific frequency range containing noise.

Analogy: Noise-canceling headphones removing engine hum.

Application: Medical imaging, MRI noise removal.

Band Pass Filters

Allows only desired frequency band to pass.

Example: Highlighting edges in fingerprint recognition.

Notch Filters

Removes single-frequency periodic noise.

Example: Removing electrical interference lines from TV images.

Optimum Notch Filtering

Advanced Concept

Balances noise removal and image preservation.

Example: NASA satellite image correction.

Inverse Filtering

Divides degraded image by degradation function.

Limitation

Noise amplification when H(u,v) ≈ 0

Example: Deblurring shaky photos.

Wiener Filtering

Why Best?

Minimizes mean square error.

Considers

  • Blur
  • Noise
  • Image statistics

Example: Medical X-ray enhancement.

Final Comparison Table

MethodBest UseDrawback
MeanLow noiseBlurring
MedianSalt & pepperSlower
AdaptiveMixed noiseComplex
InverseBlurNoise boost
WienerBlur + noiseNeeds stats

Memory Tricks

  • Mean → Average
  • Median → Middle
  • Adaptive → Smart
  • Notch → Specific
  • Wiener → Winner filter