Designing incoherent unit norm tight frames via block coordinate descent-based alternating projection

Abstract

In this paper, we introduce a novel methodology for constructing incoherent unit norm tight frames, termed block coordinate descent-based alternating projection. In the proposed approach, the underlying min-max problem was reformulated in a block-wise fashion by taking a fixed number of columns as a block and adding a spectral constraint, and it was approximately solved via an alternating projection method with Nesterov accelerated gradient technique. Numerical experiments demonstrate that the resulting algorithm is particularly efficient for the construction of incoherent unit norm tight frames with high redundancy and has great advantages in running efficiency.