A comparison of parameter choice rules for $$\ell ^p$$-$$\ell ^q$$ minimization

Abstract

Abstract Images that have been contaminated by various kinds of blur and noise can be restored by the minimization of an $$\ell ^p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>ℓ</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:math> - $$\ell ^q$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>ℓ</mml:mi><mml:mi>q</mml:mi></mml:msup></mml:math> functional. The quality of the reconstruction depends on the choice of a regularization parameter. Several approaches to determine this parameter have been described in the literature. This work presents a numerical comparison of known approaches as well as of a new one.

Topics & Concepts