A function y = sin(x) + sin(10 x) * sin(50 x) is given. I built a system matrix A that approximates this sys through the Integral of y, called Y.

Now using the LSQR algorithm, it is now possible to get y by the information in Y and A.

This is also performed using Y_noise = Y + white Gaussian (0 mean; stand. dev. = 0.3) instead of Y.

As plotted output I get:

(see attachment)

So, why does the results differ like they do. "What happens to the noise inside LSQR algorithm?"