id: 06045875
dt: j
an: 06045875
au: Bajwa, Waheed U.; Calderbank, Robert; Mixon, Dustin G.
ti: Two are better than one: fundamental parameters of frame coherence.
so: Appl. Comput. Harmon. Anal. 33, No. 1, 58-78 (2012).
py: 2012
pu: Elsevier Science (Academic Press), Orlando, FL
la: EN
cc: 
ut: frames; worst-case coherence; Welch bound; sparse signal processing
ci: 
li: doi:10.1016/j.acha.2011.09.005
ab: This paper only considers finite-dimentional frames and investigates two
    parameters that measure the coherence of a frame: worst-case and
    average coherence. The authors use them to derive near-optimal
    probabilistic guarantees on both sparse signal detection and
    reconstruction in the presence of noise, and provide a catalog of
    nearly tight frames with small worst-case and average coherence. They
    also find a new lower bound on worst-case coherence, compare it to the
    Welch bound and use it to interpret recently reported signal
    reconstruction results. Finally, they present an algorithm that
    transforms frames in a way that decreases average coherence without
    changing the spectral norm or worst-case coherence.
rv: Richard A. Zalik (Auburn)