Optical scanning holography (OSH) enables us to capture the three-dimensional information of an object, and a post-processing step known as sectional image reconstruction allows us to view its two-dimensional cross-section. Previous methods often produce reconstructed images that have blurry edges. In this paper, we argue that the hologram's two-dimensional Fourier transform maps into a semi-sp...

This paper deals with the problem of regularizing noisy fields of diffusion tensors, considered as symmetric and semi-positive definite n n matrices (as for instance 2D structure tensors or DT-MRI medical images). We first propose a simple anisotropic PDE-based scheme that acts directly on the matrix coefficients and preserve the semipositive constraint thanks to a specific reprojection step. T...

This paper presents an abstract analysis of bounded variation (BY) methods for illposed apentor equations Au = L. Let where the penalty, or 'regularization'. parameter (I > 0 and the functional J ( u ) is the BY norm or semi-norm of U , also known 3s the total variation of U. Under mild restrictions on the operator A and the functional J ( u ) , it is shown that the functional T ( u ) has a uni...

This paper presents a filtering approach for semidense probabilistic depth map received from a focused plenoptic camera. In the probabilistic depth map each valid depth pixel contains, beside the depth value itself, a variance which gives a measure for the certainty of the estimated depth. This variance is used in a weighted filtering approach. Here, beside removing outliers and filling holes i...

Dropout and other feature noising schemes control overfitting by artificially corrupting the training data. For generalized linear models, dropout performs a form of adaptive regularization. Using this viewpoint, we show that the dropout regularizer is first-order equivalent to an L2 regularizer applied after scaling the features by an estimate of the inverse diagonal Fisher information matrix....

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with mixed regularization. The first step is strictly direct and of sampling type, and faithfully detects the scatt...

In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton m...

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with nonsmooth mixed regularization. The first step is strictly direct and of sampling type, and it faithfull...

This work is concerned with L 1 data fitting for nonlinear inverse problems. This formulation is advantageous if the data is corrupted by impulsive noise. However, the problem is not differentiable and lacks local uniqueness, which makes its efficient solution challenging. By considering a regularized primal-dual formulation of this problem, local uniqueness can be shown under a second order su...

In this paper we introduce a novel variational method for joint estimation and regularization of diffusion tensor fields from noisy raw data. To this end, we use the classic quadratic data fidelity term derived from the Stejskal-Tanner equation with a new smoothness term leading to a convex objective function. The regularization term is based on the assumption that the signal can be reconstruct...