On the Minimum Condition Number of Dual Frames

In frame reconstruction, we are usually dealing with the inverse of a high-dimensional matrix. In this respect, tight frames are simpler and more valuable than other frames. In other words, when we use tight frames, it is not necessary to compute the inverse of their frame operators, and we can reconstruct vectors directly from their own frame elements. Given a frame, how can we get a frame as tight as a Parseval frame? rescaling the elements of the frame is a simple and non-invasive answer to this question. These types of frames, recently introduced by G. Kutyniok, are called scalable. For non-scalable frames, fnding the best scaling that produces a frame whose frame operator is close enough to the identity operator is an active area of research in the feld. In this talk, we present the best scaling for non-scalable frames and, by a novel approach, compute the coeffcients explicitly for some classes of frames. We also establish a criterion, called the minimum condition of frames, to compare the degree of non-scalability.

کلیدواژه ها:

Frames ، Scalable frames ، Condition number ، Tight frame ، dual frame