What is the difference / similarities between Tikhonov's regularization and the least squares method? I have tried to find information on both but can´t find any clear answers to this question, so I am having a really hard time to understand this.
To clarify: I was asked to solve a problem with Tikhonov's regularization but they had solved it with least square method, why is this possible? The task was to debug an image in python.
Edit More information: From what I understand, Tikhonov regualization is a method for solving ill-conditioned systems Ax = b and it is a regularized least squares method. And the least squares method is used to approximate solutions to systems of equations that have no solutions because they have too large a number of equations (overdetermined).
What I was going to do was use Tikhonov's regularization to deblur an image using $V=\operatorname*{argmin}_V||HV-V^{blur}||^2+\beta||V||^2$ that they described as Tikhonovs regularization, where H is the blurring matrix, $V$ is the deblur matrix and $V^{blur}$ is a matrix already given to me as well.
However, they used the command spicy.sparse.lsqr that is the least square method for solving a system Ax=b, I know how they used this command but what I don't understand is why they can use it when they specifically told us to use Tikhonov's regularization?
Thanks in advance!