Generalized cross validation for ℓp-ℓq minimization

Abstract Discrete ill-posed inverse problems arise in various areas of science and engineering. The presence noise the data often makes it difficult to compute an accurate approximate solution. To reduce sensitivity computed solution noise, one replaces original problem by a nearby well-posed minimization problem, whose is less sensitive than problem. This replacement known as regularization. We consider situation when consists fidelity term, that defined terms p -norm, regularization q -norm. allow 0 < , ≤ 2. relative importance determined parameter. paper develops automatic strategy for determining parameter these problems. proposed approach based on new application generalized cross validation. Computed examples illustrate performance method proposed.