Tight frame

Summary

A frame of a Hilbert space is a family of vectors that recovers every vector stably from its inner products with the family. Unlike a basis, a frame may be redundant. A tight frame is a frame whose lower and upper frame bounds are equal. Then reconstruction is as simple as for an orthonormal basis, up to a constant factor. Tight frames are used in signal processing, coding and quantum information, where redundancy gives robustness.