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Scaling frame vectors is a simple and noninvasive way to construct tightframes. However, not all frames can be modifed to tight frames in this fashion,so in this case we explore the problem of finding the best conditioned frame byscaling, which is crucial for applications like signal processing. We concludethat this problem is equivalent to solving a convex optimization probleminvolving the operator norm, which is unconventional since this problem wasonly studied in the perspective of Frobenious norm before. We also furtherstudy the Frobenious norm case in relation to the condition number of the frameoperator, and the convexity of optimal scalings.

Frame Scalings: A Condition Number Approach