Introduced the Full Problem of Image Restoration

  • Derived the model for the degradation function, showing that H[] is assumed to be linear and position invariant for the purposes of our stated degradation model.
  • Typically h(x,y), the degradation function is unknown, we must then estimate it.
Approach 1 for estimation of h(x,y) : Experimentation
  • Again, this is the approach where we know f(x,y) and assume that e(x,y) is neglible, i.e., e(x,y) = 0. Then g(x,y) = f(x,y)*h(x,y) (* denotes convolution).
  • We can then estimate h(x,y) easily in the fourier domain.
  • Introduce inverse filtering.
  • Demonstrate it's weaknesses and it's virtues in estimating h(x,y).
  • Revisit the definition of the point spread function (PSF).

 Approach 2 for estimation of h(x,y) : Mathematical Modeling

  • Introduced Hufnagel and Stanley's model for image distortion due to aerial turbulence  [1964].
  • Introduced a model for motion blurring, i.e., a directional PSF, due to a long exposure time for a moving object.
  • Demonstrate the application of these models on sample images to verify their effects.

Inverse Filtering

  • Demonstrate the application of  inverse filtering for the mathematical models derived in approach 2.

Weiner Filtering (Minimum Mean Square Error Filtering or MMSE)

  • Introduce the criterion to be optimized in Weiner filtering.
  • Present the solution for this criterion as the Weiner filter. Explain its departure from, and how it may reduce to inverse filtering.
  • Demonstrate Weiner filters for the two modeled mathematical systems.

Constrained Least Squares Filtering

  • Introduce the smoothness criterion and the minimum error constraint for the Constrained Least Squares filter. Explain its departure from Weiner filtering and how it may reduce to inverse filtering.
  • Describe the algorithm for implementing the filter.