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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--H\u00fcrlimann 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.<\/jats:p>","DOI":"10.1137\/130932168","type":"journal-article","created":{"date-parts":[[2014,9,17]],"date-time":"2014-09-17T13:04:59Z","timestamp":1410959099000},"page":"1775-1798","source":"Crossref","is-referenced-by-count":18,"title":["Solving 2D Fredholm Integral from Incomplete Measurements Using Compressive Sensing"],"prefix":"10.1137","volume":"7","author":[{"given":"Alexander","family":"Cloninger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wojciech","family":"Czaja","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruiliang","family":"Bai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter J.","family":"Basser","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,9,17]]},"reference":[{"key":"atypb1","unstructured":"B. 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