# 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} }

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…

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## References

SHOWING 1-10 OF 57 REFERENCES

Laplace deconvolution with noisy observations

- Mathematics
- 2011

In the present paper we consider Laplace deconvolution for discrete noisy data observed on the interval whose length may increase with a sample size. Although this problem arises in a variety of…

Input Recovery from Noisy Output Data, Using Regularized Inversion of the Laplace Transform

- MathematicsIEEE Trans. Inf. Theory
- 1998

It appears that there exists a natural, unbiased, estimator for the La place transform of the output, from which an estimator of the input can be obtained by multiplication with the polynomial and subsequent application of a regularized inverse of the Laplace transform.

Wavelet deconvolution in a periodic setting

- Mathematics
- 2004

Summary. Deconvolution problems are naturally represented in the Fourier domain, whereas thresholding in wavelet bases is known to have broad adaptivity properties. We study a method which combines…

PENALIZED CONTRAST ESTIMATOR FOR DENSITY DECONVOLUTION

- 2005

We consider the problem of estimating the density g of independent and identically distributed variables Xi, from a sample Z1, . . . , Zn where Zi = Xi + σεi, i = 1, . . . , n, ε is a noise…

Wavelet decomposition approaches to statistical inverse problems

- Mathematics
- 1998

SUMMARY A wide variety of scientific settings involve indirect noisy measurements where one faces a linear inverse problem in the presence of noise. Primary interest is in some function f(t) but data…

Future Polynomial Regularization of Ill-Posed Volterra Equations

- MathematicsSIAM J. Numer. Anal.
- 2000

The future polynomial regularization method discussed here may be applied to quite general operator equations provided that the operator may be discretized by a lower-triangular matrix of Toeplitz type.

On deconvolution with repeated measurements

- Mathematics
- 2008

In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this…

Deconvolution-Based CT and MR Brain Perfusion Measurement: Theoretical Model Revisited and Practical Implementation Details

- Computer ScienceInt. J. Biomed. Imaging
- 2011

This paper presents a comprehensive derivation and explanation of the underlying physiological model for intravascular tracer systems, and discusses the need for regularization in order to obtain physiologically reasonable results.