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This problem has been considered recently for Gaussian measurement noise, and here we develop this idea with application to Poisson systems. A collaborative maximum likelihood algorithm and alternating proximal gradient algorithm are proposed, and associated theoretical performance guarantees are established based on newly derived concentration-of-measure results. A Bayesian model is then introduced, to improve flexibility and generality. Connections between the maximum likelihood methods and the Bayesian model are developed, and example results are presented for a real compressive X-ray imaging system.<\/jats:p>","DOI":"10.1137\/140998779","type":"journal-article","created":{"date-parts":[[2015,9,17]],"date-time":"2015-09-17T19:11:01Z","timestamp":1442517061000},"page":"1923-1954","source":"Crossref","is-referenced-by-count":12,"title":["Signal Recovery and System Calibration from Multiple Compressive Poisson Measurements"],"prefix":"10.1137","volume":"8","author":[{"given":"Liming","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaji","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xin","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kalyani","family":"Krishnamurthy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joel","family":"Greenberg","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Volkan","family":"Cevher","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miguel R. 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