Look at the Optimization Function:
$$ \hat{x} = \arg \min_{x} {\| Hx -y \|}^{2} + \lambda {\| G x \|}_{1} $$
Where $ H $ is the Blur Operator and $ G $ is the Derivative Operator.
Now, you can look at it in the Sparse sense or you can look at it as the MAP solution given a Laplace prior for the Gradient.
Anyhow, to validate this assumption, make a simple observation, take a real world image (Moderate level of noise).
Calculate it gradient and watch its histogram.
It will easily jump...