<p>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.</p>

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A Computational Approach to the Minimum Condition Number of Frames

  • Behine Heydarpour,
  • Ali Akbar Arefijamaal,
  • Fahimeh Arabyani-Neyshaburi

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.