Constrained regularization with the L1 norm for ill-posed problems

Many advances in modern science and technology have resulted in linear ill-posed problems, whose operator form is Kf = g, with possibly some constraints on the solution (e.g. non-negativity). The prototype example is a Fredholm integral equation of the first kind. An effective and prominent approach to cope with the instability of these problems is known as regularization. Most existing regularization methods are based on the L2 norm and this approach is now well-developed. This thesis aims to develop a practical, general regularization method using the Li norm in both unconstrained and linearly constrained cases..