Generalized cross validation for ℓ p - ℓ q minimization

AbstractDiscrete ill-posed inverse problems arise in various areas of science and engineering. The presence of noise in the data often makes it difficult to compute an accurate approximate solution. To reduce the sensitivity of the computed solution to the noise, one replaces the original problem by a nearby well-posed minimization problem, whose solution is less sensitive to the noise in the data than the solution of the original problem. This replacement is known as regularization. We consider the situation when the minimization problem consists of a fidelity term, that is defined in terms of ap-norm, and a regularization term, that is defined in terms of aq-norm. We allow 0