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Here, the blur length was L = 9, and the blurred image A1 was obtained by
executing the following commands:

A1=A*B;
imagesc(A1,[0 1])
To bring back the unblurred picture, simply multiply the matrix A1 on the
right by inv(B) and obtain the original image.
In practice, one is given the blurred image and asked to reconstruct it while
correcting for the blur. What to do?
1. Compute the blur length from the plane speed and height.
2. Construct the Toeplitz matrix, and take its inverse.
3. Apply the inverse of the Toeplitz matrix to the blurred image
matrix, obtaining the processed image.

9.3.3 Encrypting an Image
If for any reason, two individuals desire to exchange an image but want to
keep its contents only to themselves, they may agree beforehand on a scram-
bling matrix that the first individual applies to scramble the sent image, while
the second individual applies the inverse of the scramble matrix to unscram-
ble the received image.
Given that an average quality image currently has a minimum size of about
(1000×1000) pixels, reconstructing the scrambling matrix, if chosen cleverly,
would be inaccessible except to the most powerful and specialized computers.
The purpose of the following problems is to illustrate an efficient method
for building a scrambling matrix.

In-Class Exercises

Assume for simplicity that the 2-D array size is (10×10), and that the scram-
bling matrix is chosen such that each row has one element equal to 1, while
the others are 0, and no two rows are equal.
Pb. 9.15 For the (10×10) matrix dimension, how many possible scrambling
matrices S, constructed as per the above prescription, are there? If the matrix
size is (1000×1000), how many such scrambling matrices will there be?

Pb. 9.16 An original figure was scrambled by the scrambling matrix S to
obtain the image shown in Figure 9.2. The matrix S is (10×10) and has all its
elements equal to zero, except S(1, 6) = S(2, 3) = S(3, 2) = S(4, 1) = S(5, 9) =
S(6, 4) = S(7, 10) = S(8, 7) = S(9, 8) = S(10, 5) = 1. Find the original image.

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