18-793 Image and Video Processing
Submission instructions.
Submissions are due on Thursday 11/05 at 10.00pm ET
Please upload scans of your solution in GradeScope (via Canvas)
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Homework 8
Instructions
Please solve all non-MATLAB problems using only paper and pen, without resorting to
a computer.
Please show all necessary steps to get the final answer. However, there is no need to be overly elaborate. Crisp and complete answers.
For all MATLAB problems, include all code written to generate solutions.
Please post all questions on the discussion board on the Piazza course website.
If you feel some information is missing, you are welcome to make reasonable assumptions and proceed. Sometimes the omissions are intentional. Needless to say, only reasonable assumptions will be accepted.
1. (Iterative Hard Thresholding)
Implement iterative hard thresholding in MATLAB under wavelet sparsity prior. Your function for iterative hard thresholding that solves the problem
min 1∥y − A(x)∥2 s.t ∥Ψ(x)∥0 ≤ K, x2
might look like this
function xstar = IHT(y, K, Psi, PsiAdj, A, AAdj, MaxIter, xinit)
Here xinit is an initial guess of the solution.
Deliverable 1. Matlab function for IHT. Please label the code for readability.
Deliverable 2. Use the code below to test your code. You should include the completed code and the figure it generates.
Homework 8
clear all; close all
N = 1024; %Signal dimension
M = 256; %%number of measurements! 256 < 1024!!
K = 64; %sparsity level
x0 = zeros(N, 1);
Supp0 = randperm(N, K); %support of sparse signal
x0(Supp0) = randn(K, 1); %%sparse signal
A = randn(M, N)/sqrt(M); %%measurement matrix
y = A*x0; %%measurements
%%%%[Your code goes here]
%%setup function handles and other variables
%%call IHT and get output in the variable xstar
%%Visualize results
stem(x0); hold on
stem(xstar, ’rx’);
2. (Inpainting with Iterative Hard Thresholding)
We will test the code from the problem above on the inpainting problem.
In hw8.mat, you are given a grayscale image in the variable corrupted and a mask image mask that indicate where the corruptions are. Inpaint with IHT.
Deliverable 1. For the inpainting problem , provide MATLAB code for implementing the operator A and its adjoint A∗.
Deliverable 2. Describe your strategy for initialization. Think of something clever =)
Deliverable 3. Inpaint the image for using your IHT code. Do sweep through values of K for best results. In your submission you are expected to show the restored image. You will be evaluated on the quality of the reconstructed image.
3. (Deblurring with Iterative Hard Thresholding)
Repeat Problem 2 for the deblurring problem.
In hw8.mat, you are given a grayscale image in the variable blurred and a blurring kernel k0. Here, the unknown sharp image is related to the blurred image via a convolution with the blurring kernel.
Deblur with IHT.
Homework 8 3 Deliverable 1. For the deblurring problem , provide MATLAB code for implementing
the operator A and its adjoint A∗.
Deliverable 2. Describe your strategy for initialization. Think of something clever =)
Deliverable 3. Deblur the image for using your IHT code. Do sweep through values of K for best results. In your submission you are expected to show the restored image. You will be evaluated on the quality of the reconstructed image.
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