Designing Incoherent Frames With Only Matrix–Vector Multiplications

Designing frames with low mutual coherence is a challenging problem, with many applications in signal processing. We adopt an atom-by-atom optimization strategy for obtaining frames with a given mutual coherence. The underlying min-max problem is transformed into a weighted least squares problem, approximately solved with the shifted power method. The resulting algorithm is extremely simple, works directly with the frame and consists of almost only matrix-vector multiplications. Numerical experiments shows that it is especially efficient for frames with a large overcompleteness factor and can design in reasonable time frames much larger than those obtained by other existing methods.