The Orthogonal Matching Pursuit (OMP) for compressed sensing iterates over a scheme of support augmentation and signal estimation. We present two novel matching pursuit algorithms with intrinsic regularization of the signal estimation step that do not rely on a priori knowledge of the signal's sparsity. An iterative approach allows for a hardware efficient implementation of our algorithm, and enables real-world applications of compressed sensing. We provide a series of numerical examples that demonstrate a good performance, especially when the number of measurements is relatively small.