{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T07:22:43Z","timestamp":1781162563893,"version":"3.54.1"},"reference-count":48,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows one to recover this signal from much fewer samples than the Shannon\u2013Nyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms and others. Generally, wavelets represent point-like features while curvelets represent line-like features well. For a suitable recovery of images, we propose models that contain weighted sparsity constraints in two different frames. Given the incomplete measurements f = \u03a6u + \u03f5 with the measurement matrix \u03a6 \u2208 \u211d<jats:sup>K \u00d7 N<\/jats:sup>, K \u226a N, we consider a jointly sparsity-constrained optimization problem of the form [Formula: see text]. Here \u03a8<jats:sub>c<\/jats:sub>and \u03a8<jats:sub>w<\/jats:sub>are the transform matrices corresponding to the two frames, and the diagonal matrices \u039b<jats:sub>c<\/jats:sub>, \u039b<jats:sub>w<\/jats:sub>contain the weights for the frame coefficients. We present efficient iteration methods to solve the optimization problem, based on Alternating Split Bregman algorithms. The convergence of the proposed iteration schemes will be proved by showing that they can be understood as special cases of the Douglas\u2013Rachford Split algorithm. Numerical experiments for compressed sensing-based Fourier-domain random imaging show good performances of the proposed curvelet-wavelet regularized split Bregman (CWSpB) methods, where we particularly use a combination of wavelet and curvelet coefficients as sparsity constraints.<\/jats:p>","DOI":"10.1142\/s0219691311003955","type":"journal-article","created":{"date-parts":[[2011,2,1]],"date-time":"2011-02-01T05:42:47Z","timestamp":1296538967000},"page":"79-110","source":"Crossref","is-referenced-by-count":50,"title":["CURVELET-WAVELET REGULARIZED SPLIT BREGMAN ITERATION FOR COMPRESSED SENSING"],"prefix":"10.1142","volume":"09","author":[{"given":"GERLIND","family":"PLONKA","sequence":"first","affiliation":[{"name":"Institute for Numerical and Applied Mathematics, University of G\u00f6ttingen, Lotzestr. 16-18, 37083 G\u00f6ttingen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"JIANWEI","family":"MA","sequence":"additional","affiliation":[{"name":"School of Aerospace, Tsinghua University, Beijing 100084, P. 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