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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

This paper investigates motion tracking for ultrasound imaging. The proposed method is adapted to ultrasonic images and uses a bilinear motion model for controlling the local mesh deformation. We use an iterative multi-scale approach which is shown to considerably decrease the estimated motion error when we pass from 1 to 2 iterations. The proposed algorithm is tested in two medical applications. First, we use it to track tissue motion for ultrasound elastography. The second application is related to slow blood flow estimation with high frequency ultrasound imaging. In both cases, our technique considerably improves the quality of the results compared to classical block matching (BM).

Parametric Deformable Block Matching for Ultrasound Imaging

A new Plug-and-Play (PnP) alternating direction of multipliers (ADMM) scheme is proposed in this paper, by embedding a recently introduced adaptive denoiser using the Schroedinger equation’s solutions of quantum physics. The potential of the proposed model is studied for Poisson image deconvolution, which is a common problem occurring in number of imaging applications, such as limited photon acquisition or X-ray computed tomography. Numerical results show the efficiency and good adaptability of the proposed scheme compared to recent state-of-the-art techniques, for both high and low signal-to-noise ratio scenarios. This performance gain regardless of the amount of noise affecting the observations is explained by the flexibility of the embedded quantum denoiser constructed without anticipating any prior statistics about the noise, which is one of the main advantages of this method. The main novelty of this work resided in the integration of a modified quantum denoiser into the PnP-ADMM framework and the numerical proof of convergence of the resulting algorithm.

Plug-and-Play Quantum Adaptive Denoiser for Deconvolving Poisson Noisy Images

This paper proposes a method of 2-D translations estimation using an a priori signal model. Two analytical signals defined with multidimensional Hilbert transform are considered and shown to have linear phases with respect to the translations to estimate. A least squares estimator (LSE) is then developed to adjust the measured phases of the complex signals to their theoretical forms. Moreover, the LSE provides an analytical solution to the 2-D translation estimation problem. The estimator is then included in a block matching method for motion tracking with ultrasound images. We compared our results with those obtained with a classical sum of absolute differences (SAD) cost function. We show that with our method there is no need of interpolating the images. Thus, for images at the original resolution level, the results obtained with the proposed estimator are largely more accurate than with SAD. Moreover, we show that using SAD on images with resolution five times higher provide roughly the same results as with our method, but the processing time is ten times higher in this case.

Two-dimensional least-squares estimation for motion tracking in ultrasound elastography

High-resolution ultrasound (US) image reconstruction from a reduced number of measurements is of great interest in US imaging, since it could enhance both frame rate and image resolution. Compressive deconvolution (CD), combining compressed sensing and image deconvolution, represents an interesting possibility to consider this challenging task. The model of CD includes, in addition to the compressive sampling matrix, a 2-D convolution operator carrying the information on the system point spread function. Through this model, the resolution of reconstructed US images from compressed measurements mainly depends on three aspects: the acquisition setup, i.e., the incoherence of the sampling matrix, the image regularization, i.e., the sparsity prior, and the optimization technique. In this paper, we mainly focused on the last two aspects. We proposed a novel simultaneous direction method of multipliers based optimization scheme to invert the linear model, including two regularization terms expressing the sparsity of the RF images in a given basis and the generalized Gaussian statistical assumption on tissue reflectivity functions. The performance of the method is evaluated on both simulated and in vivo data.

https://hal.archives-ouvertes.fr/hal-01484966/document

Reconstruction of Enhanced Ultrasound Images From Compressed Measurements Using Simultaneous Direction Method of Multipliers

Ultrasound (US) imaging accompanies each of us, from several months before we are born, throughout our lives. This chapter presents both the physical basics of US imaging and the main advances expected of the echography of tomorrow. It begins with a presentation of the physical principles upon which US imaging is based. Then, it details the different modes of imaging in US systems: B-mode, M-mode, Doppler modes, contrast and harmonic imaging. The hardware aspects are also touched upon, with a discussion of the different types of linear or sectorial probes used in clinical practice, depending on the compromise between resolution and penetration. The chapter discusses statistical analysis of the US image using the properties of the US speckle. The final part of the chapter is devoted to the advances in US image acquisition and processing which can serve as a diagnostic aid to doctors.

Adrian Basarab

Papers

Parametric Deformable Block Matching for Ultrasound Imaging

Plug-and-Play Quantum Adaptive Denoiser for Deconvolving Poisson Noisy Images

Two-dimensional least-squares estimation for motion tracking in ultrasound elastography

Reconstruction of Enhanced Ultrasound Images From Compressed Measurements Using Simultaneous Direction Method of Multipliers

Ultrasound Medical Imaging