Consider:
x a $N \times 1$ vector , with elements $x_i$
b a $N \times 1$ vector , with elements $b_i$
A a $M \times N$ matrix , with elements $a_{ij}$ ( Symmetric matrix - Block Circulant )
As we know , the Euclidean-Vector norm of an equation $f={||Ax+b||}^2$ is:
$${(Ax+b)}^T(Ax+b)$$ where $T$ indicates the Transposed form of a vector.
I have faced some difficulties studying about Image Restoration , with the Constrained Least Squares filter specifically , finding the proof that the first derivative of the above equation $f$ with respect to x is:
$$ \frac{\partial}{\partial x}\ {||Ax+b||}^2 = 2A^T (Ax+b) $$
I would be grateful if i could have some help!
Thank you in advance!