Abstract. Tikhonov regularization often is applied with a finite difference regularization operator that approximates a low-order derivative. This paper proposes the use of orthogonal projections as regularization operators, e.g., with the same null space as commonly used finite difference operators. Applications to iterative and SVD-based methods for Tikhonov regularization are described. Truncated iterative and SVD methods are also considered. Key words. ill-posed problem, regularization operator, orthogonal projection, Tikhonov regularization, truncated iteration, SVD, GSVD.