Stamatios Lefkimmiatis

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Inverse problems with shot noise arise in many modern biomedical imaging applications. The main challenge is to obtain an estimate of the underlying specimen from measurements corrupted by Poisson noise. In this work, we propose an efficient framework for ...

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which a ...

In this paper we introduce a new reconstruction algorithm for X-ray differential phase-contrast Imaging (DPCI). Our approach is based on 1) a variational formulation with a weighted data term and 2) a variable-splitting scheme that allows for fast converge ...

We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functional ...

We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our ...

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second- ...

We develop a variational algorithm for reconstructing phase objects from a series of bright field micrographs. Our mathematical model is based on the transport-of-intensity equation (TIE), which links the phase of a complex field to the axial derivative of ...

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupt ...

In this paper, we propose a novel second-order regularizer based on the maximum response of the second-order directional derivative, assuming that the image under consideration belongs to the class of piecewise-linear signals. Compared to total-variation r ...

Stamatios Lefkimmiatis

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3D Poisson Microscopy Deconvolution With Hessian Schatten-Norm Regularization

Hessian Schatten-Norm Regularization for Linear Inverse Problems

Constrained regularized reconstruction of X-ray-DPCI tomograms with weighted-norm

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Digital Phase Reconstruction via Iterative Solutions of Transport-of-Intensity Equation

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

A Second-Order Extension Of Tv Regularization For Image Deblurring