On the choice of regularization matrix for an ?2-? minimization method for image restoration

Ill-posed problems arise in many areas of science and engineering. Their solutions, if they exist, are very sensitive to perturbations the data. To reduce this sensitivity, original problem may be replaced by a minimization with fidelity term regularization term. We consider kind, which is square ?2-norm discrepancy qth power ?q-norm size computed solution measured some manner. interested situation when 0<q?1, because such choice q promotes sparsity solution. The determined matrix. Novati Russo let q=2 proposed (2014) [13] matrix that finite difference approximation differential operator applied approximate after reordering. This gives Tikhonov general form. show also well suited for 0<q?1. Applications image restoration presented.