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Regularization Of Inverse Problems

The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis-Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.

Riemann manifold Langevin and Hamiltonian Monte Carlo methods

Super-resolution, the process of obtaining one or more high-resolution images from one or more low-resolution observations, has been a very attractive research topic over the last two decades. It has found practical applications in many real-world problems in different fields, from satellite and aerial imaging to medical image processing, to facial image analysis, text image analysis, sign and number plates reading, and biometrics recognition, to name a few. This has resulted in many research papers, each developing a new super-resolution algorithm for a specific purpose. The current comprehensive survey provides an overview of most of these published works by grouping them in a broad taxonomy. For each of the groups in the taxonomy, the basic concepts of the algorithms are first explained and then the paths through which each of these groups have evolved are given in detail, by mentioning the contributions of different authors to the basic concepts of each group. Furthermore, common issues in super-resolution algorithms, such as imaging models and registration algorithms, optimization of the cost functions employed, dealing with color information, improvement factors, assessment of super-resolution algorithms, and the most commonly employed databases are discussed.

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Super-resolution: a comprehensive survey

Cengage Learning, 2000. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary:

Applied Nonparametric Statistics

Cardiac motion estimation from ultrasound images is an ill-posed problem that needs regularization to stabilize the solution. In this work, regularization is achieved by exploiting the sparseness of cardiac motion fields when decomposed in an appropriate dictionary, as well as their smoothness through a classical total variation term. The main contribution of this work is to robustify the sparse coding step in order to handle anomalies, i.e., motion patterns that significantly deviate from the expected model. The proposed approach uses an ADMM-based optimization algorithm in order to simultaneously recover the sparse representations and the outlier components. It is evaluated using two realistic simulated datasets with available ground-truth, containing native outliers and corrupted by synthetic attenuation and clutter artefacts.

/pdf/cardiac-motion-estimation-with-dictionary-learning-and-381h05fq16.pdf

Cardiac motion estimation with dictionary learning and robust sparse coding in ultrasound imaging

The first part of this paper presents some works conducted with Jose Bioucas Dias for fusing high spectral resolution images (such as hyperspectral images) and high spatial resolution images (such as panchromatic or multispectral images) in order to build images with improved spectral and spatial resolutions These works are related to Bayesian fusion strategies exploiting prior information about the target image to be recovered constructed by dictionary learning Interestingly, these Bayesian image fusion methods can be adapted with limited changes to motion estimation in pairs or sequences of images The second part of this paper explains how the work of Jose Bioucas Dias has been a source of inspiration for developing new Bayesian motion estimation methods for ultrasound images

Sparse Representations and Dictionary Learning: from Image Fusion to Motion Estimation

In this paper, a 2D least square FIR differentiation filter method is proposed in the context of tensorial elastography Displacements are estimated from ultrasonic images obtained during freehand compression Two 2D filters are used for providing all partial derivative maps according to the estimated motion obtained with a Bilinear Deformable Block Matching method From these results, several strain tensor images are built, revealing the tissue's elasticity properties Among these tensors, the infinitesimal strains, the rigid rotation and principal strains tensors are retained, thus improving the contrast between the tumor and the background tissue The 2D filters were first applied to displacement maps estimated from simulated data and two experimental RF data sets and then compared to the 1D differentiation filter LSQSE used in elastography The first experimental data set was collected from a homogeneous phantom with a cylindrical hard inclusion and the second data set was collected from a thyroid gland with a malignant tumor For all studied RF data sets, the contrast between the tumor and the background tissue calculated on strain tensor maps was increased up to a factor of 3 with our method compared to the LSQSE method We also observed that the rigid rotation tensor and principal strains tensor were well adapted to thyroid elastography

A 2D least square differentiation filter for tensorial elastography

Aircraft certification procedures require the estimation of wing deformation, which is a very challenging problem in photogrammetry applications. Indeed, in real flight conditions with varying environment, 3D reconstruction is strongly degraded. To cope with this issue, we propose to introduce prior knowledge about the wing mechanical limits in the photogrammetry reconstruction method. These mechanical limits are expressed as appropriate regularizations that are included into the classical bundle adjustment step. The proposed approach is evaluated using data acquired on a real aircraft yielding promising results.

/pdf/constrained-bundle-adjustment-applied-to-wing-3d-2j540fplse.pdf

Constrained Bundle Adjustment Applied To Wing 3d Reconstruction With Mechanical Limitations

This paper proposes a novel framework to reconstruct the dynamic magnetic resonance images (DMRI) with motion compensation (MC). Due to the inherent motion effects during DMRI acquisition, reconstruction of DMRI using motion estimation/compensation (ME/MC) has been studied under a compressed sensing (CS) scheme. In this paper, by embedding the intensity-based optical flow (OF) constraint into the traditional CS scheme, we are able to couple the DMRI reconstruction with motion field estimation. The formulated optimization problem is solved by a primal-dual algorithm with linesearch due to its efficiency when dealing with non-differentiable problems. With the estimated motion field, the DMRI reconstruction is refined through MC. By employing the multi-scale coarse-to-fine strategy, we are able to update the variables(temporal image sequences and motion vectors) and to refine the image reconstruction alternately. Moreover, the proposed framework is capable of handling a wide class of prior information (regularizations) for DMRI reconstruction, such as sparsity, low rank and total variation. Experiments on various DMRI data, ranging from in vivo lung to cardiac dataset, validate the reconstruction quality improvement using the proposed scheme in comparison to several state-of-the-art algorithms.

Adrian Basarab

Papers

Cardiac motion estimation with dictionary learning and robust sparse coding in ultrasound imaging

Sparse Representations and Dictionary Learning: from Image Fusion to Motion Estimation

A 2D least square differentiation filter for tensorial elastography

Constrained Bundle Adjustment Applied To Wing 3d Reconstruction With Mechanical Limitations

Motion Compensated Dynamic MRI Reconstruction with Local Affine Optical Flow Estimation