A tight frame in a Hilbert space is a collection 
for which there is a constant
such that
 |
for every vector 
in the space. Unlike an orthonormal
basis, a tight frame may be redundant. Nevertheless, every vector
has the reconstruction
 |
A tight frame with 
is called a Parseval frame. Tight frames are used in signal processing because redundancy
can provide robustness while retaining a simple reconstruction formula (Duffin and
Schaeffer 1952, Christensen 2016).
