My question comes from image processing community,
In our Machine Learning algorithm, we have a predicted value $D$ and its equivalent ground truth $D^*$
where their difference is: $d_i=D-D^*$.
(Think about each of them as a matrix containing all the pixel values of an image)
Now, our goal is to minimize the following objective function:
$L(D,D^*)=\frac{1}{n}\sum_{i}d_i^2-\frac{1}{2n^2}(\sum_{i} d_i)^2+\frac{1}{n}\sum_{i}[(\nabla_xd_i)^2+(\nabla_yd_i)^2]$
where $\nabla_xd_i$ and $\nabla_yd_i$ are the horizontal and vertical gradients of the difference.
For further details see the paper.
What can be the derivative of $L$ w.r.t. $D\; ?$ $(\frac{\partial L}{\partial D} = ?)$
Actually, I have a headache with the last term.
Many thanks in advance.
P.S.: if the 3rd term in unclear, let's check the answer for the first and the second terms.