Homeworks

5th Homework:
 Type: Simulation
 Computer program: Implement Basis Pursuit method for finding the sparse solution of un underdetermined linear system. You can use this guide.
 Due date: Friday 95/3/21.

4th Homework:
 Type: Simulation
 Computer program: Implement the BSS method based on mutual information minimization. For estimating score functions, use two methods: polynomial and kernel estimators. For the iterations, use both equivariant and nonequivariant (usual steepest descent) and compare their sensitivity versus the conditioning of the mixing matrix.
 Due date: Sunday 95/2/26.

3rd Homework:
 Type: Simulation
 Computer program: Implement EASI algorithm and use it to separate two mixed images signals. Your program has to be in the form of a MATLAB function:
[y1,y2]= separate(x1,x2);
x1 and x2, each one of is mixture of two image signals. The function takes them, and gives us y1 and y2, which have to be separated images. To test the function, you load in MATLAB two images (s1 and s2), mix them (for example using x1=0.8*s1+0.2*s2; x2=0.2*s1+ 0.8*s2) and then give x1 and x2 to the above function to get y1 and y2. Then you visually compare y1 and y2 with s1 and s2. (for example by seeing them using "imshow" function).
Measure the difference between separated and original images using SNR in dB, defined as (assuming that you have no permutation, that is, y1 is an estimation of s1 not an estimation of s2):
SNR = 10 * log10 (mean(s1.^2) / mean( (s1y1).^2 ) )
and include these SNR's in your report. Usually you arrive around 30dB (or at least above 20dB). You can also plot SNR versus iteration.
 Due date: Tuesday 95/2/7.

2nd Homework:
 Type: Manual
 Problems 3.3, 3.4, 4.1, 4.2, 4.7, 4.9, 4.11, 4.13, 4.18 of Hyvarinen's book.
 Due date: Sunday 95/1/15.

1st Homework:
 Type: 6 manual problems PLUS one computer program.
 Manual part: Problems 2.2, 2.7, 2.9, 2.12, 2.15, 2.24 of Hyvarinen's book.
 Computer program: Write a MATLAB program to compute the kurtosis of a random variable from its sampples. Test you routine on U(0,1) and N(0,1) random variables, and compare the results with true values.
 Due date: Tuesday 94/12/18.