A Computational Approach to the Minimum Condition Number of Frames
摘要
Scalable frames in Hilbert spaces are essential tools in signal processing due to their ability to provide flexible and robust representations of data. For non-scalable frames, finding 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 field. In this paper, we investigate the best scaling for non-scalable frames and, using a novel approach, compute their coefficients explicitly for some classes of frames. We also establish a criterion, called the minimum condition of frames, to compare the degree of non-scalability. In particular, we obtain a concrete formula for the minimum condition of Riesz bases with respect to their elements.