Construction of unimodular tight frames for compressed sensing using majorization-minimization

In this paper, we propose a method to construct uni-modular tight frames (UMTFs), which are tight frames with the additional constraint that every entry of the matrix has the same magnitude. UMTFs are useful in many applications, since multiplication of a UMTF by a vector can be implemented in polar coordinates using very low computational cost. Since normalized UMTFs are unit norm tight frames (UNTFs), and since a UNTF is a minimizer of the...