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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

The resolution of ultrasound images is limited by the bandwidth of the imaging system and the features of the propagating medium. Using certain assumptions, image restoration can recover out-of-bandwidth data and improve resolution. Several resolution improvement methods have been reported in the literature. However, due to the lack of ground truth, their evaluation on experimental data remains an open issue. Indeed, to evaluate the performance of such methods, knowledge of the scattering function is necessary. Usually this is achieved with numerical simulations, since in traditional phantoms the exact distribution of scatterers is unknown. In the current work, based on a 3D-printed phantom, the feasibility of the evaluation of deconvolution is investigated. The deconvolution method used lp-norm-regularization terms with p=0.5 and p=2. Knowledge of the scattering function allows comparison of the deconvolved images with the ground truth. Thus, using the scattering function and the originally acquired B-mode image, performance of image restoration methods could be evaluated quantitatively through comparison of root mean square error and full width half maximum values. Preliminary results demonstrate the benefits of knowing the scattering function during experimental testing of image restoration methods. In summary, the current work shows the potential of an experimental method for evaluating the extent to which an image restoration method provides a faithful rendering of the underlying scattering structure.

/pdf/validation-of-image-restoration-methods-on-3d-printed-4nkstgwrg0.pdf

Validation of image restoration methods on 3D-printed ultrasound phantoms

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.

Joint Dynamic MRI Reconstruction and Aggregated Motion Estimation with Optical Flow Constraint.

Speckle has a considerable impact on medical ultrasound (US) imaging due to its its intrinsic random nature and spatially correlated behavior that severely reduces image contrast. In this paper, leveraging the quantum many-body theory, we propose a deep-learning architecture recasting a baseline denoising algorithm for adaptive contrast enhancement of US images. The proposed deep neural network integrates quantum mechanical concepts based on Schrödinger equations which makes our model robust for US image restoration. The potential of the proposed deep unfolded network is illustrated on simulated data and clinical cardiac US images. Both results show enhanced images with improved contrast and resolution while preserving underlying structures and significantly reducing the speckle noise.

Adaptive Contrast Enhancement of Cardiac Ultrasound Images using a Deep Unfolded Many-Body Quantum Algorithm

This paper proposes a new motion estimation method based on convolutional sparse coding to adaptively design the colored-coded apertures in static and dynamic spectral videos. The motion in a spectral video is estimated from a low-resolution reconstruction of the datacube by training a convolutional dictionary per spectral band and solving a minimization problem. Simulations show improvements in terms of peak signal-to-noise ratio (of up to 2 dB) of the reconstructed videos by using the proposed approach, compared with state-of-art non-adaptive coded apertures.

/pdf/adaptive-coded-aperture-design-by-motion-estimation-using-34f4elxq17.pdf

Adrian Basarab

Papers

Validation of image restoration methods on 3D-printed ultrasound phantoms

Joint Dynamic MRI Reconstruction and Aggregated Motion Estimation with Optical Flow Constraint.

Adaptive Contrast Enhancement of Cardiac Ultrasound Images using a Deep Unfolded Many-Body Quantum Algorithm

Adaptive Coded Aperture Design by Motion Estimation using Convolutional Sparse Coding in Compressive Spectral Video Sensing