Monotonicity of data fidelity and regularization penalty
= Monotonicity of data fidelity and regularization penalty
For $0<\alpha<\beta$, choosing <global minimizers> of $D+\alpha J$ and $D+\beta J$ gives $J(u_\beta)\leq J(u_\alpha)$ and $D(u_\beta)\geq D(u_\alpha)$. The decrease in penalty and increase in data misfit satisfy $\alpha\Delta J\leq\Delta D\leq\beta\Delta J$.