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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.

/pdf/super-resolution-a-comprehensive-survey-xjl42yt9nt.pdf

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

This paper introduces a new fusion method for magnetic resonance (MR) and ultrasound (US) images, which aims at combining the advantages of each modality, i.e., good contrast and signal to noise ratio for the MR image and good spatial resolution for the US image. The proposed algorithm is on an inverse problem, performing a super-resolution of the MR image and a denoising of the US image. A polynomial function is introduced to model the relationships between the gray levels of the MR and US images. The resulting inverse problem is solved using a proximal alternating linearized minimization algorithm. The accuracy and the interest of the fusion algorithm are shown quantitatively and qualitatively via evaluations on synthetic and experimental phantom data.

/pdf/fusion-of-magnetic-resonance-and-ultrasound-images-for-5bvppe3xrm.pdf

Fusion of Magnetic Resonance and Ultrasound Images for Endometriosis Detection

https://hal.archives-ouvertes.fr/hal-01567077/document

Strong reflector-based beamforming in ultrasound medical imaging.

This paper addresses the problem of high-resolution Doppler blood flow estimation from an ultrafast sequence of ultrasound images. Formulating the separation of clutter and blood components as an inverse problem has been shown in the literature to be a good alternative to spatio-temporal singular value decomposition (SVD)-based clutter filtering. In particular, a deconvolution step has recently been embedded in such a problem to mitigate the influence of the experimentally measured point spread function (PSF) of the imaging system. Deconvolution was shown in this context to improve the accuracy of the blood flow reconstruction. However, measuring the PSF requires non-trivial experimental setups. To overcome this limitation, we propose herein a blind deconvolution method able to estimate both the blood component and the PSF from Doppler data. Numerical experiments conducted on simulated and in vivo data demonstrate qualitatively and quantitatively the effectiveness of the proposed approach in comparison with the previous method based on experimentally measured PSF and two other state-of-the-art approaches.

Joint Blind Deconvolution and Robust Principal Component Analysis for Blood Flow Estimation in Medical Ultrasound Imaging

This paper introduces a novel computationally efficient method of solving the 3D single image super-resolution (SR) problem, i.e., reconstruction of a high-resolution volume from its low-resolution counterpart. The main contribution lies in the original way of handling simultaneously the associated decimation and blurring operators, based on their underlying properties in the frequency domain. In particular, the proposed decomposition technique of the 3D decimation operator allows a straightforward implementation for Tikhonov regularization, and can be further used to take into consideration other regularization functions such as the total variation, enabling the computational cost of state-of-the-art algorithms to be considerably decreased. Numerical experiments carried out showed that the proposed approach outperforms existing 3D SR methods.

A Novel Fast 3D Single Image Super-Resolution Algorithm

It has been recently shown that compressive sampling is an interesting perspective for fast ultrasound imaging. This paper addresses the problem of compressive deconvolution for ultrasound imaging systems using an assumption of generalized Gaussian distributed tissue reflectivity function. The benefit of compressive deconvolution is the joint volume reduction of the acquired data and the image resolution improvement. The main contribution of this work is to apply the framework of compressive deconvolution on ultrasound imaging and to propose a novel l p -norm (1 ≤ p ≤ 2) algorithm based on Alternating Direction Method of Multipliers. The performance of the proposed algorithm is tested on simulated data and compared with those obtained by a more intuitive sequential compressive deconvolution method.

/pdf/ultrasound-compressive-deconvolution-with-l-p-norm-prior-lngzzyg65p.pdf

Adrian Basarab

Papers

Fusion of Magnetic Resonance and Ultrasound Images for Endometriosis Detection

Strong reflector-based beamforming in ultrasound medical imaging.

Joint Blind Deconvolution and Robust Principal Component Analysis for Blood Flow Estimation in Medical Ultrasound Imaging

A Novel Fast 3D Single Image Super-Resolution Algorithm

Ultrasound compressive deconvolution with ℓ P -Norm prior