The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Medical Image Computing and Computer-Assisted Intervention

Rise of silicene: A competitive 2D material

Low-dose computed tomography (LDCT) images are often severely degraded by amplified mottle noise and streak artifacts These artifacts are often hard to suppress without introducing tissue blurring effects In this paper, we propose to process LDCT images using a novel image-domain algorithm called "artifact suppressed dictionary learning (ASDL)" In this ASDL method, orientation and scale information on artifacts is exploited to train artifact atoms, which are then combined with tissue feature atoms to build three discriminative dictionaries The streak artifacts are cancelled via a discriminative sparse representation operation based on these dictionaries Then, a general dictionary learning processing is applied to further reduce the noise and residual artifacts Qualitative and quantitative evaluations on a large set of abdominal and mediastinum CT images are carried out and the results show that the proposed method can be efficiently applied in most current CT systems

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Artifact suppressed dictionary learning for low-dose CT image processing.

Retinal vessel segmentation using a probabilistic tracking method

Magnetic resonance imaging (MRI) is corrupted by Rician noise, which is image dependent and computed from both real and imaginary images. Rician noise makes image-based quantitative measurement difficult. The non-local means (NLM) filter has been proven to be effective against additive noise. Considering the characteristics of both Rician noise and the NLM filter, this study proposes a frame for a pre-smoothing NLM (PSNLM) filter combined with image transformation. In the PSNLM frame, noisy MRI is first transformed into an image in which noise can be treated as additive noise. Second, the transformed MRI is pre-smoothed via a traditional denoising method. Third, the NLM filter is applied to the transformed MRI, with weights that are computed from the pre-smoothed image. Finally, inverse transformation is performed on the denoised MRI to obtain the denoising results. To test the performance of the proposed method, both simulated and real patient data are used, and various pre-smoothing (Gaussian, median, and anisotropic filters) and image transformation [squared magnitude of the MRI, and forward and inverse variance-stabilizing trans-formations (VST)] methods are used to reduce noise. The performance of the proposed method is evaluated through visual inspection and quantitative comparison of the peak signal-to-noise ratio of the simulated data. The real data include Alzheimer’s disease patients and normal controls. For the real patient data, the performance of the proposed method is evaluated by detecting atrophy regions in the hippocampus and the parahippocampal gyrus. The comparison of the experimental results demonstrates that using a Gaussian pre-smoothing filter and VST produce the best results for the peak signal-to-noise ratio (PSNR) and atrophy detection.

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Brain MR image denoising for Rician noise using pre-smooth non-local means filter

GVFOM: a novel external force for active contour based image segmentation

The total variation (TV) model is one kind of second-order partial differential equation (PDE) for image noise removal However, the second-order PDEs suffer from the so-called staircase effect Proposed is a modified TV (MTV) model, which is staircase-free by minimising the variation of the image along the direction tangential to the isophotes of the original image Its effectiveness in preserving edges, avoiding staircases and removing noises is shown by experiment and comparison

MTV: modified total variation model for image noise removal

Purpose: A robust, automatic, and rapid method for liver delineation is urgently needed for the diagnosis and treatment of liver disorders. Until now, the high variability in liver shape, local image artifacts, and the presence of tumors have complicated the development of automatic 3D liver segmentation. In this study, an automatic three-level AdaBoost-guided active shape model (ASM) is proposed for the segmentation of the liver based on enhanced computed tomographyimages in a robust and fast manner, with an emphasis on the detection of tumors. Methods: The AdaBoost voxel classifier and AdaBoost profile classifier were used to automatically guide three-level active shape modeling. In the first level of model initialization, fast automatic liver segmentation by an AdaBoost voxel classifier method is proposed. A shape model is then initialized by registration with the resulting rough segmentation. In the second level of active shape model fitting, a prior model based on the two-class AdaBoost profile classifier is proposed to identify the optimal surface. In the third level, a deformable simplex mesh with profile probability and curvature constraint as the external force is used to refine the shape fitting result. In total, three registration methods—3D similarity registration, probability atlas B-spline, and their proposed deformable closest point registration—are used to establish shape correspondence. Results: The proposed method was evaluated using three public challenge datasets: 3Dircadb1, SLIVER07, and Visceral Anatomy3. The results showed that our approach performs with promising efficiency, with an average of 35 s, and accuracy, with an average Dice similarity coefficient (DSC) of 0.94 ± 0.02, 0.96 ± 0.01, and 0.94 ± 0.02 for the 3Dircadb1, SLIVER07, and Anatomy3 training datasets, respectively. The DSC of the SLIVER07 testing and Anatomy3 unseen testing datasets were 0.964 and 0.933, respectively. Conclusions: The proposed automatic approach achieves robust, accurate, and fast liver segmentation for 3D CTce datasets. The AdaBoost voxel classifier can detect liver area quickly without errors and provides sufficient liver shape information for model initialization. The AdaBoost profile classifier achieves sufficient accuracy and greatly decreases segmentation time. These results show that the proposed segmentation method achieves a level of accuracy comparable to that of state-of-the-art automatic methods based on ASM.

Fast automatic 3D liver segmentation based on a three-level AdaBoost-guided active shape model.

X-ray angiography, a powerful technique for the visualization of blood vessels, has been widely used in clinical practice. However, due to unavoidable motion of patient, the subtraction images often suffer from misregistration artifacts. In order to improve the quality of subtraction images, registration algorithms are often employed before direct subtraction of mask and live images. A novel multiresolution elastic registration algorithm is proposed for the registration of the digital angiographic images using thin-plate spline (TPS). Our main contribution is a multiresolution search strategy specifically designed for the template matching method. In this strategy, the mask image is decomposed to coarse and fine sub-image blocks iteratively using the pyramid approach. Experimental results show that the multiresolution refinement strategy is well adapted to the template matching method, and can achieve better performance than comparable single step algorithms, because local minima can be overcome by the gradual coarse-to-fine approach that also ensures convergence. Registration results of four typical similarity measures, namely energy of histogram of differences (EHD), mutual information (MI), correlation and sum of squared differences (SSD), are compared. Three different interpolation methods, including nearest-neighbor, bilinear and bicubic, are also tested and compared. The overall conclusion is that the multiresolution refinement algorithm based on EHD combined with the bicubic interpolation method is very robust and effective for the registration of X-ray angiography images, which can obtain sub-pixel registration accuracy and is fully automatic. In addition, the objective measurement method developed in this paper on simulated data makes it possible to quantitatively evaluate the quality of the elastic registration results

Shoujun Zhou

Papers

Brain MR image denoising for Rician noise using pre-smooth non-local means filter

GVFOM: a novel external force for active contour based image segmentation

MTV: modified total variation model for image noise removal

Fast automatic 3D liver segmentation based on a three-level AdaBoost-guided active shape model.

Multiresolution Elastic Registration of X-Ray Angiography Images Using Thin-Plate Spline