Pointwise adaptive estimation for robust and quantile regression

A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds are obtained, which yield rate-optimality for large sample asymptotics under weak conditions. Simulations for different univariate median regression models show good finite sample properties, also in comparison to traditional methods. The approach is extended to image denoising and applied to CT scans in cancer research

Laplace deconvolution and its application to Dynamic Contrast Enhanced imaging

In the present paper we consider the problem of Laplace deconvolution with noisy discrete observations. The study is motivated by Dynamic Contrast Enhanced imaging using a bolus of contrast agent, a procedure which allows considerable improvement in {evaluating} the quality of a vascular network and its permeability and is widely used in medical assessment of brain flows or cancerous tumors. Although the study is motivated by medical imaging application, we obtain a solution of a general problem of Laplace deconvolution based on noisy data which appears in many different contexts. 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 Laguerre functions basis. The expansion results in a small system of linear equations with the matrix of the system being triangular and Toeplitz. The number $m$ of the terms in the expansion of the estimator is controlled via complexity penalty. The advantage of this methodology is that it leads to very fast computations, does not require exact knowledge of the kernel and produces no boundary effects due to extension at zero and cut-off at $T$. The technique leads to an estimator with the risk within a logarithmic factor of $m$ of the oracle risk under no assumptions on the model and within a constant factor of the oracle risk under mild assumptions. The methodology is illustrated by a finite sample simulation study which includes an example of the kernel obtained in the real life DCE experiments. Simulations confirm that the proposed technique is fast, efficient, accurate, usable from a practical point of view and competitive

Quantifying tumor vascular heterogeneity with DCE-MRI in complex adnexal masses: A preliminary study

International audiencePurpose: To evaluate the value of quantifying dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) heterogeneity to characterize adnexal masses.Materials and Methods: Our database was retrospectively queried to identify all surgically proven adnexal masses characterized with a 1.5T DCE-MRI between January 1st 2008 and February 28th 2010 (n = 113 masses, including 52 benign, 11 borderline, and 50 invasive malignant tumors). The solid component of the adnexal mass was segmented. Quantitative analysis with a compartmental model was performed to calculate microvascular parameters, including tissue blood flow (FT), blood volume fraction (Vb), lag time (DAT), interstitial volume fraction (Ve), permeability–surface area product (PS), and relative area under curve (rAUC), were calculated. Then heterogeneity parameters were evaluated using the analysis of the evolution of the standard deviation (SD) of signal intensities on DCE-MRI series. The area under the receiver operating characteristic (AUROC) curve was calculated to assess the overall discrimination of parameters.Results: Malignant tumors displayed higher FT, Vb, and rAUC and lower DAT than benign tumors (P = 0.01, P < 0.0001, and P < 0.0001, respectively). Invasive malignant tumors displayed lower Vb and rAUC than borderline tumors (P < 0.01). After injection, whenever the heterogeneity parameter was considered, malignant tumors were more heterogeneous than benign tumors, invasive tumors were more heterogeneous than borderline ovarian tumors, and malignant tumors with carcinomatosis were more heterogeneous than tumors without carcinomatosis (P < 0.001). The most discriminant parameter was the SD during the 90 seconds after injection related to arterial input function (ΔSDEARLY/AIF) with an AUROC between 0.715 and 0.808.Conclusion: This study proposes heterogeneity parameters as a new tool with a potential for clinical application, given that the technique uses routine imaging sequences

Early modifications of hepatic perfusion measured by functional CT in a rat model of hepatocellular carcinoma using a blood pool contrast agent

Macromolecular contrast-enhanced functional CT was performed to characterize early perfusion changes in hepatocellular carcinoma (HCC). Fourteen rats with chemically induced primary liver tumors ranging pathologically from hyperplasia to HCC and 15 control rats were investigated. Two dynamic CT scans using an experimental macromolecular contrast agent were performed on a single slice 11 and 18 weeks after tumor induction followed by pathological examination. A deconvolution mathematical model was applied, yielding the hepatic perfusion index (HPI), mean transit time (MTT), liver distribution volume (LDV) and arterial, portal and total blood flows (FA, FP, FT). Analysis was performed on one slice per rat, containing overall two hyperplasia, six dysplasia and 15 HCC. On the first scans, HCC at an early pathological stage had a low FP (-30%, P=0.002) but a normal arterial-portal balance. On the scan contemporary to pathology, HCC perfusion parameters showed an inversion of the arterial-portal balance (HPI +212%,