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We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex if and only if posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images. Parts of this work have been presented at conferences [M. Seeger, H. Nickisch, R. Pohmann, and B. Sch\u00f6lkopf, in Advances in Neural Information Processing Systems 21, D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, eds., Curran Associates, Red Hook, NY, 2009, pp. 1441\u20131448; H. Nickisch and M. Seeger, in Proceedings of the 26th International Conference on Machine Learning, L. Bottou and M. Littman, eds., Omni Press, Madison, WI, 2009, pp. 761\u2013768].<\/jats:p>","DOI":"10.1137\/090758775","type":"journal-article","created":{"date-parts":[[2011,3,4]],"date-time":"2011-03-04T13:23:17Z","timestamp":1299244997000},"page":"166-199","source":"Crossref","is-referenced-by-count":31,"title":["Large Scale Bayesian Inference and Experimental Design for Sparse Linear Models"],"prefix":"10.1137","volume":"4","author":[{"given":"Matthias W.","family":"Seeger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hannes","family":"Nickisch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,3,3]]},"reference":[{"key":"R1","unstructured":"H. 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