Recently, three independent works suggested iterated shrinkage algorithms that generalizes the classic work by Donoho and Johnston. Daubechies, Defrise and De-Mol developed such an algorithm for deblurring, using the concept of surrogate functions. Figueirido and Nowak used the EM algorithm to construct such algorithm, and later extended their work by using the bound-optimization technique. Elad developed such an algorithm based on a parallel coordinate descent (PCD) point of view. In this talk we describe these methods with an emphasis on the later, and demonstrate how it can be of importance for the minimization of a general basis pursuit penalty function. As such, the proposed algorithms form a new pursuit technique, falling in between the basis pursuit and the matching pursuit.