The label set is $\$ where 0 means the original pixels should be used and 1 means the computed average should be used.
The energy functional decomposes into a dataterm $\phi$ and a smoothness term $\psi$: A hard threshold on $D^i_$ can be achieved by using some appropriate set of $\alpha, \beta_0, \beta_1$.
Again, to make the algorithm more robust against noise, the sum of color differences around a Gaussian patch is used instead.
(Assuming zero-mean noise, the sum of differences around the same patch should be close to zero.) This threshold alone can cause noisy artifacts, so we simply enforce spatial smoothness using Markov random field defined on a standard 4-connected grid.
In such case, it is sometimes more desirable to retain the noisy original pixels.
One way to solve this problem is to apply a threshold to the color difference and retain original pixels when the sum is too large.
We perspective-warp each frame to the reference by robustly solving for a 3 x 3 homography via RANSAC.
Then we run polynomial expansion-based Farneback's optical flow algorithm between each frame and the reference which is fast and gives low interpolation error but has high endpoint and angular errors.
This gives us a baseline quality for denoising algorithms.
The runtime however turns out to be impractical for real-time applications as the algorithm took 23 minutes to process 15 frames at resolution 960 x 540 pixels.