TY - JOUR
T1 - Nonuniform sampling, image recovery from sparse data and the discrete sampling theorem
AU - Yaroslavsky, Leonid F.
AU - Shabat, Gil
AU - Salomon, Benjamin G.
AU - Ideses, Ianir A.
AU - Fishbain, Barak
PY - 2009/3/1
Y1 - 2009/3/1
N2 - In many applications, sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases, it is necessary to convert irregularly sampled signals to regularly sampled ones or to restore missing data. We address this problem in the framework of a discrete sampling theorem for band-limited discrete signals that have a limited number of nonzero transform coefficients in a certain transform domain. Conditions for the image unique recovery, from sparse samples, are formulated and then analyzed for various transforms. Applications are demonstrated on examples of image superresolution and image reconstruction from sparse projections.
AB - In many applications, sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases, it is necessary to convert irregularly sampled signals to regularly sampled ones or to restore missing data. We address this problem in the framework of a discrete sampling theorem for band-limited discrete signals that have a limited number of nonzero transform coefficients in a certain transform domain. Conditions for the image unique recovery, from sparse samples, are formulated and then analyzed for various transforms. Applications are demonstrated on examples of image superresolution and image reconstruction from sparse projections.
UR - http://www.scopus.com/inward/record.url?scp=63349111488&partnerID=8YFLogxK
U2 - 10.1364/JOSAA.26.000566
DO - 10.1364/JOSAA.26.000566
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AN - SCOPUS:63349111488
SN - 1084-7529
VL - 26
SP - 566
EP - 575
JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision
JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision
IS - 3
ER -