On Optimal Frame Conditioners
For researchers in frame theory and signal processing, this work offers a new convex optimization perspective on constructing optimally conditioned tight frames.
The paper reformulates the problem of frame scalability as a convex optimization problem and provides numerical results on randomly generated frames, demonstrating the effectiveness of the proposed methods.
A (unit norm) frame is scalable if its vectors can be rescaled so as to result into a tight frame. Tight frames can be considered optimally conditioned because the condition number of their frame operators is unity. In this paper we reformulate the scalability problem as a convex optimization question. In particular, we present examples of various formulations of the problem along with numerical results obtained by using our methods on randomly generated frames.