Laplace Deconvolution On The Basis Of Time Domain Data And Its Application To Dynamic Contrast-Enhanced Imaging

Keywords

Complexity penalty; Dynamic contrast-enhanced imaging; Laplace deconvolution; LaplaceDeconv R package; Model selection; Perfusion imaging

Abstract

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→∞). 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.

Publication Date

1-1-2017

Publication Title

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volume

79

Issue

1

Number of Pages

69-94

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1111/rssb.12159

Socpus ID

84960968367 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84960968367

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