{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T15:57:51Z","timestamp":1791475071611,"version":"4.3.4"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T00:00:00Z","timestamp":1676592000000},"content-version":"vor","delay-in-days":2550,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1106564"],"award-info":[{"award-number":["DMS-1106564"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1407475"],"award-info":[{"award-number":["DMS-1407475"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,1,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over a Laguerre functions basis (which acts as a surrogate eigenfunction basis of the Laplace convolution operator) using a regression setting. The expansion results in a small system of linear equations with the matrix of the system being triangular and Toeplitz. Because of this triangular structure, there is a common number m of terms in the function expansions to control, which is realized via a complexity penalty. The advantage of this methodology is that it leads to very fast computations, produces no boundary effects due to extension at zero and cut-off at T and provides an estimator with the risk within a logarithmic factor of m of the oracle risk. We emphasize that we consider the true observational model with possibly non-equispaced observations which are available on a finite interval of length T which appears in many different contexts, and we account for the bias associated with this model (which is not present in the case T \u2192 \u221e). The study is motivated by perfusion imaging using a short injection of contrast agent, a procedure which is applied for medical assessment of microcirculation within tissues such as cancerous tumours. The presence of a tuning parameter a allows the choice of the most advantageous time units, so that both the kernel and the unknown right-hand side of the equation are well represented for the deconvolution. The methodology is illustrated by an extensive simulation study and a real data example which confirms that the technique proposed is fast, efficient, accurate, usable from a practical point of view and very competitive.<\/jats:p>","DOI":"10.1111\/rssb.12159","type":"journal-article","created":{"date-parts":[[2016,2,26]],"date-time":"2016-02-26T08:09:50Z","timestamp":1456474190000},"page":"69-94","source":"Crossref","is-referenced-by-count":31,"title":["Laplace Deconvolution on the Basis of Time Domain Data and its Application to Dynamic Contrast-Enhanced Imaging"],"prefix":"10.1093","volume":"79","author":[{"given":"Fabienne","family":"Comte","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris Descartes, Sorbonne , Paris Cit\u00e9 , France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Charles-A.","family":"Cuenod","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris Descartes and European Hospital G. 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