Projection to the Set of Shift Orthogonal Functions
  This paper presents a fast algorithm for projecting a given function to the set of shift orthogonal functions (i.e. set containing functions with unit $L^2$ norm that are orthogonal to their prescribed shifts). The algorithm can be parallelized easily and its computational complexity is bounded by $O(M\log(M))$, where $M$ is the number of coefficients used for storing the input. To derive the algorithm, a particular class of basis called Shift Orthogonal Basis Functions are introduced and some theory regarding them is developed. 
Farzin Barekat, Rongjie Lai, Ke Yin, Stanley Osher, Russel Caflisch,   Vidvuds Ozolins
math.NA math-ph math.MP math.OC