To Do: image denoising in wavelet domain

Section: Inverse Problems

Data

Images you want (you can use Barbara provided in the Fourier section)

To do

  • Simulate various inpainting problem as follow
    • Generate a random binary matrix A of the same size of the image, with a parameter $p$ controling the bernoulli law
    • Add some white gaussian noise (at various level)
    • Generate the direct problem $y = Ax + b$ (where $x$ is the original image)
  • Estimate $x$ using the sparse approach (reminder: an image is sparse in the wavelet domain)
  • Discuss the results obtained by changing:
    • the sparse respresentation (various wavelet orhtogonal transform and translation invariant wavelets)
    • the thresholding rules (soft, hard, empirical Wiener)
    • the choice of the $\lambda$ parameter
    • Discussion whould be made with respect to the value of $p$ and the level of noise