Construction of finite tight frames via singular value decomposition

Finite tight frames are used widely for many applications. An important problem is to construct finite frames containing specified elements as needed in real world applications. In this paper we provide a stable method for that purpose. We establish an identity for constructing equi-norm tight frames from the specified elements and present a method for generating equi-norm tight frames explicitly from the outcome of the singular value decomposition of the matrix of the given elements. Under certain conditions, the number of columns of the unit-norm tight frames generated by our method reaches the minimum bound, improving a result in the literature. Finally, we illustrate our method through a numerical example