Solving 2D Fredholm Integral from Incomplete Measurements Using Compressive Sensing.
SIAM J Imaging Sci
; 7(3): 1775-1798, 2014.
Article
em En
| MEDLINE
| ID: mdl-34267858
ABSTRACT
We present an algorithm to solve the two-dimensional Fredholm integral of the first kind with tensor product structure from a limited number of measurements, with the goal of using this method to speed up nuclear magnetic resonance spectroscopy. This is done by incorporating compressive sensing-type arguments to fill in missing measurements, using a priori knowledge of the structure of the data. In the first step we recover a compressed data matrix from measurements that form a tight frame, and establish that these measurements satisfy the restricted isometry property. Recovery can be done from as few as 10% of the total measurements. In the second and third steps, we solve the zeroth-order regularization minimization problem using the Venkataramanan-Song-Hürlimann algorithm. We demonstrate the performance of this algorithm on simulated data and show that our approach is a realistic approach to speeding up the data acquisition.
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MEDLINE
Idioma:
En
Revista:
SIAM J Imaging Sci
Ano de publicação:
2014
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Article