• DOI:10.1111/rssb.12159
• Corpus ID: 88519911

Laplace deconvolution on the basis of time domain data and its application to dynamic contrast‐enhanced imaging

@article{Comte2014LaplaceDO,
  title={Laplace deconvolution on the basis of time domain data and its application to dynamic contrast‐enhanced imaging},
  author={Fabienne Comte and Charles Andr{\'e} Cu{\'e}nod and Marianna Pensky and Yves Rozenholc},
  journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  year={2014},
  volume={79}
}

• F. Comte, C. Cuénod, +1 author Y. Rozenholc
• Published 28 May 2014
• Mathematics
• Journal of the Royal Statistical Society: Series B (Statistical Methodology)

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.