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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

Image resolution enhancement is a problem of considerable interest in all medical imaging modalities. Unlike general purpose imaging or video processing, for a very long time, medical image resolution enhancement has been based on optimization of the imaging devices. Although some recent works purport to deal with image postprocessing, much remains to be done regarding medical image enhancement via postprocessing, especially in ultrasound imaging. We face a resolution improvement issue in the case of medical ultrasound imaging. We propose to investigate this problem using multidimensional autoregressive (AR) models. Noting that the estimation of the envelope of an ultrasound radio frequency (RF) signal is very similar to the estimation of classical Fourier-based power spectrum estimation, we theoretically show that a domain change and a multidimensional AR model can be used to achieve super-resolution in ultrasound imaging provided the order is estimated correctly. Here, this is done by means of a technique that simultaneously estimates the order and the parameters of a multidimensional model using relevant regression matrix factorization. Doing so, the proposed method specifically fits ultrasound imaging and provides an estimated envelope. Moreover, an expression that links the theoretical image resolution to both the image acquisition features (such as the point spread function) and a postprocessing feature (the AR model) order is derived. The overall contribution of this work is threefold. First, it allows for automatic resolution improvement. Through a simple model and without any specific manual algorithmic parameter tuning, as is used in common methods, the proposed technique simply and exclusively uses the ultrasound RF signal as input and provides the improved B-mode as output. Second, it allows for the a priori prediction of the improvement in resolution via the knowledge of the parametric model order before actual processing. Finally, to achieve the previous goal, while classical parametric methods would first estimate the model order and then the model parameters, our approach estimates the model parameters and the order simultaneously. The effectiveness of the methodology is validated using two-dimensional synthetic and in vivo data. We show that, compared to other techniques, our method provides better results from a qualitative and a quantitative viewpoint.

/pdf/resolution-enhancement-in-medical-ultrasound-imaging-3j8is2k545.pdf

Resolution enhancement in medical ultrasound imaging.

In this paper, we address the problem of high-resolution flow estimation in medical ultrasound images. Imaging methods based on ultrafast sequences associated with adaptive spatiotemporal SVD clutter filtering have recently improved blood flow detection. Herein, we investigate a new way of addressing the clutter filtering problem in order to obtain a high-resolution flow estimation, through solving an inverse problem corresponding to both deconvolution and robust principal component analysis. Applied to tissue vascularization imaging via power Doppler images, the proposed method highlights finer details on experimental data compared to existing approaches.

/pdf/high-resolution-and-high-sensitivity-blood-flow-estimation-3ac51z866e.pdf

High-resolution and high-sensitivity blood flow estimation using optimization approaches with application to vascularization imaging

Validation of image processing techniques such as endodontic segmentations in cone-beam computed tomography (CBCT) is a challenging issue because of the lack of ground truth in in vivo experiments. The purpose of our study was to design an artificial surrounding tissues phantom able to provide CBCT image quality of real extracted teeth, similar to in vivo conditions. Note that these extracted teeth could be previously scanned using micro computed tomography (μCT) to access true quantitative measurements of the root canal anatomy. Different design settings are assessed in our study by comparison to in vivo images, in terms of the contrast-to-noise ratio (CNR) obtained between different anatomical structures. Concerning the root canal and the dentine, the best design setup allowed our phantom to provide a CNR difference of only 3% compared to clinical cases.

/pdf/cone-beam-computed-tomography-contrast-validation-of-an-7zc6az2ano.pdf

Cone-Beam Computed Tomography contrast validation of an artificial periodontal phantom for use in endodontics

Approximate Message Passing (AMP) is an iterative reconstruction algorithm that performs signal denoising within a compressive sensing framework. We propose the use of heavy tailed distribution based image denoising, specifically using a Cauchy prior based Maximum A-Posteriori (MAP) estimate within a wavelet based AMP compressive sensing structure. The use of this MAP denoising algorithm provides extremely fast convergence for image based compressive sensing. The proposed method converges approximately twice as fast as the compared AMP methods whilst providing superior final MSE results over a range of measurement rates.

/pdf/compressive-imaging-using-approximate-message-passing-and-a-4pc2i6fng9.pdf

Compressive imaging using approximate message passing and a Cauchy prior in the wavelet domain

In the last four years, a few research groups worked on the feasibility of compressive sampling (CS) in ultrasound medical imaging and several attempts of applying the CS theory may be found in the recent literature. In particular, it was shown that using iotap-norm minimization with p different from 1 provides interesting RF signal reconstruction results. In this paper, we propose to further improve this technique by processing the reconstruction in the Fourier domain. In addition, alpha -stable distributions are used to model the Fourier transforms of the RF lines. The parameter p used in the optimization process is related to the parameter alpha obtained by modelling the data (in the Fourier domain) as an alpha -stable distribution. The results obtained on experimental US images show significant reconstruction improvement compared to the previously published approach where the reconstruction was performed in the spatial domain.

Adrian Basarab

Papers

Resolution enhancement in medical ultrasound imaging.

High-resolution and high-sensitivity blood flow estimation using optimization approaches with application to vascularization imaging

Cone-Beam Computed Tomography contrast validation of an artificial periodontal phantom for use in endodontics

Compressive imaging using approximate message passing and a Cauchy prior in the wavelet domain

Medical ultrasound image reconstruction using compressive sampling and lp-norm minimization