Homework 1- Model based reconstructions

Homework 1- Model based reconstructions#

For this homework, you can use the Ippy software package both in the Virtuale page of the course and on Davide Evangelista github. The software contains some tools for some image rsonstriuction tasks from a model-based perspective. You can obviously integrate it with your own code.

Choose some grayscale images (NOT CAMERAMAN or the ones used during the lessons) and test them on

  1. denoise

  2. deblur

  3. super resolution

  4. CT image reconstruction

For each of the previous tasks:

  • create a test problem, changing both the parameters of the operator and the noise level

  • solve with a model-based regularization method by using the regularization functions discussed during the lessons:

    • Tikhonov

    • Total Variation (TV)

    • Total-p Variation (TpV) with \(0<p<1\)

  • Choose the regularization parameter :

    • by means of the Discrepancy Principle

    • as the best possible choice with respect to a metric (PSN, SSIM or Relative Error)

Required outputs and discussion

  • Visualize the input image, the reconstructions with eventually zoomed areas.

  • Plots of metrics with respect to the iterations

  • tables with the metrics obtained …. other output that you consider important for the discussion.