1,721,090 research outputs found
Matrix completion for matrices with low-rank displacement. ETNA - Electronic Transactions on Numerical Analysis
Full text linkThe matrix completion problem consists in the recovery of a low-rank or approximately low-rank matrix from a sampling of its entries. The solution rank is typically unknown, and this makes the problem even more challenging. However, for a broad class of interesting matrices with so-called displacement structure, the originally ill-posed completion problem can find an acceptable solution by exploiting the knowledge of the associated displacement rank. The goal of this paper is to propose a variational non-convex formulation for the low-rank matrix completion problem with low-rank displacement and to apply it to important classes of medium-large scale structured matrices. Experimental results show the effectiveness and efficiency of the proposed approach for Toeplitz and Hankel matrix completion problems
Sparsity-inducing variational shape partitioning
No full textAbstract. We propose a sparsity-inducing multi-channel multiple region model for the efficient partitioning
of a mesh into salient parts. Our approach is based on rewriting the Mumford-Shah models in terms of piece-wise
smooth/constant functionals that incorporate a non-convex regularizer for minimizing the boundary lengths. The
solution of this optimization problem, obtained by an efficient proximal forward backward algorithm, is used by a
simple thresholding/clusterization procedure to segment the shape into the required number of parts. Therefore, it is
not necessary to further solve the optimization problem for a different number of partitioning regions. Experimental
results show the effectiveness and efficiency of our proposals when applied to both single- and multi-channel (shape
characterizing) functions
A meshless strategy for shape diameter analysis
No full textAn approach to computing an intuitive local thickness from surface meshes was introduced with the
shape diameter function (SDF) in Shapira et al. (Vis Comput 24(4):249–259, 2008). In this paper, we present a new
dynamic approach to the computation of the SDF for a cloud of points on the boundary of a volumetric object.We employ
a particle flow driven by a simple collision test. The resulting SDF scalar field can be naturally exploited as a shape property for the volume-oriented object decomposition. Experimental results show the effectiveness and efficiency of our proposals
Constrained TVp - l2 Model for Image Restoration
No full textThe popular total variation (TV) model for image restoration (Rudin et al. in Phys D 60(1–4):259-268, 1992) can be formulated as a Maximum A Posteriori estimator which uses a half-Laplacian image-independent prior favoring sparse image gradients. We propose a generalization of the TV prior, referred to as TVp, based on a half-generalized Gaussian distribution with shape parameter p. An automatic estimation of p is introduced so that the prior better fits the real images’ gradient distribution; we will show that, in general, the estimated p value does not necessarily require to be close to zero. The restored image is computed by using an alternating directions methods of multipliers procedure. In this context, a novel result in multivariate proximal calculus is presented which allows for the efficient solution of the proposed model. Numerical examples show that the proposed approach is particularly efficient and well suited for images characterized by a wide range of gradient distributions.The popular total variation (TV) model for image restoration (Rudin et al. in Phys D 60(1–4):259-268, 1992) can be formulated as a Maximum A Posteriori estimator which uses a half-Laplacian image-independent prior favoring sparse image gradients. We propose a generalization of the TV prior, referred to as TVp, based on a half-generalized Gaussian distribution with shape parameter p. An automatic estimation of p is introduced so that the prior better fits the real images’ gradient distribution; we will show that, in general, the estimated p value does not necessarily require to be close to zero. The restored image is computed by using an alternating directions methods of multipliers procedure. In this context, a novel result in multivariate proximal calculus is presented which allows for the efficient solution of the proposed model. Numerical examples show that the proposed approach is particularly efficient and well suited for images characterized by a wide range of gradient distributions
A forward-backward strategy for handling non-linearity in Electrical Impedence Tomography
No full textElectrical Impedance Tomography (EIT) is known
to be a nonlinear and ill-posed inverse problem. Conventional
penalty-based regularization methods rely on the linearized
model of the nonlinear forward operator. However, the linearized
problem is only a rough approximation of the real situation,
where the measurements can further contain unavoidable noise.
The proposed reconstruction variational framework allows to
turn the complete nonlinear ill-posed EIT problem into a sequence
of regularized linear least squares optimization problems
via a forward-backward splitting strategy, thus converting the ill-posed
problem to a well-posed one. The framework can easily integrate
suitable penalties to enforce smooth or piecewise-constant
conductivity reconstructions depending on prior information.
Numerical experiments validate the effectiveness and feasibility
of the proposed approach
Deformation by discrete elastica
No full textModeling a physically plausible deformation of a flexible object from its naturally planar (curved) state is a fun-
damental and challenging topic in digital surface processing with applications to computer animation and game
design. We propose a new variational model for detail preserving surface-based deformation of a body based on
total curvature energy. We demonstrate the efficacy of the model with several examples which enhance the realism
of the deformation
Quantum median filter for total variation image denoising
Full text linkIn this new computing paradigm, named quantum computing, researchers from all over
the world are taking their first steps in designing quantum circuits for image process-
ing, through a difficult process of knowledge transfer. This effort is named quantum
image processing, an emerging research field pushed by powerful parallel comput-
ing capabilities of quantum computers. This work goes in this direction and proposes
the challenging development of a powerful method of image denoising, such as the
total variation (TV) model, in a quantum environment. The proposed quantum TV is
described and its sub-components are analysed. Despite the natural limitations of the
current capabilities of quantum devices, the experimental results show a competitive
denoising performance compared to the classical variational TV counterpar
A Variational Approach to Additive Image Decomposition into Structure, Harmonic, and Oscillatory Components
Full text linkWe propose a nonconvex variational decomposition model which separates a given image into piecewise-constant, smooth, and oscillatory components. This decomposition is motivated not only by image denoising and structure separation, but also by shadow and spot light removal. The proposed model clearly separates the piecewise-constant structure and smoothly varying harmonic part, thanks to having a separated oscillatory component. The piecewise-constant part is captured by TV-like nonconvex regularization, harmonic term via second-order regularization, and oscillatory (noise and texture) term via a H^{-1}-norm penalty. There are interesting interactions between these three regularization terms. We explore the effects of each regularization and the choice of parameters carefully. We propose an efficient alternating direction method of multipliers based minimization for fast numerical computation of the optimization problem. Various experiments are presented to show the robustness against a high level of noise, applications to soft spotlight and shadow removal, and the comparisons with other methods
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