Low signal to noise ratio (SNR) remains one of the limitations of diffusion weighted (DW) imaging. How to suppress the influence of noise on the subsequent analysis about the tissue microstructure is still challenging. This work proposed a novel self-supervised learning model, Replace2Self, to effectively reduce spatial correlated noise in DW images. Specifically, a voxel replacement strategy based on similar block matching in Q-space was proposed to destroy the correlations of noise in DW image along one diffusion gradient direction. To alleviate the signal gap caused by the voxel replacement, an image mixing strategy based on complementary mask was designed to generate two different noisy DW images. After that, these two noisy DW images were taken as input, and the non-correlated noisy DW image after voxel replacement was taken as learning target, a denoising network was trained for denoising. To promote the denoising performance, a complementary mask mixing consistency loss and an inverse replacement regularization loss were also proposed. Through the comparisons against several existing DW image denoising methods on extensive simulation data with different noise distributions, noise levels and b-values, as well as the acquisition datasets and the ablation experiments, we verified the effectiveness of the proposed method. Regardless of the noise distribution and noise level, the proposed method achieved the highest PSNR, which was at least 1.9% higher than the suboptimal method when the noise level reaches 10%. Furthermore, our method has superior generalization ability due to the use of the proposed strategies.

Considering the tumor aggressive nature and the significant changes in anatomical structure, aligning the preoperative and follow up scans of glioma patients remains a challenge due to the presence of regions with absent correspondence. To address this challenge, this work proposed a novel bidirectional unsupervised deformable image registration framework for image pairs with missing correspondence based on an auxiliary-image-aided intensity-consistency constraint (ICC) strategy. Specifically, for any fixed and moving image pairs, we introduced an auxiliary image and warped it directly to fixed/moving image or warped it twice through a transition of moving/fixed image. By comparing the difference between these warped images, the weighting maps to identify and exclude regions with absent correspondence between fixed and moving image pairs can be generated. To verify the effectiveness of the proposed framework, we combined it with several deep learning-based registration models and tested it on BraTS-Reg challenge dataset, the results demonstrated that the proposed ICC strategy can improve the registration performance for all the models, with the improvement of average target registration error (TRE) and success rate (SR) being up to 44.9% and 66.7%, respectively. Comparing against the best existing forward-backward consistency strategy for dealing with missing correspondence registration, our auxiliary-image-aided ICC strategy can also decrease average TRE by 2.9%, demonstrating the superiority of the proposed framework. The present work is not limited to the glioma images, it can be used to address the registration problems for any image pairs with absent correspondence or inconsistent intensity.

To promote the generalization ability of breast tumor segmentation models, as well as to improve the segmentation performance for breast tumors with smaller size, low-contrast and irregular shape, we propose a progressive dual priori network (PDPNet) to segment breast tumors from dynamic enhanced magnetic resonance images (DCE-MRI) acquired at different centers. The PDPNet first cropped tumor regions with a coarse-segmentation based localization module, then the breast tumor mask was progressively refined by using the weak semantic priori and cross-scale correlation prior knowledge. To validate the effectiveness of PDPNet, we compared it with several state-of-the-art methods on multi-center datasets. The results showed that, comparing against the suboptimal method, the DSC and HD95 of PDPNet were improved at least by 5.13% and 7.58% respectively on multi-center test sets. In addition, through ablations, we demonstrated that the proposed localization module can decrease the influence of normal tissues and therefore improve the generalization ability of the model. The weak semantic priors allow focusing on tumor regions to avoid missing small tumors and low-contrast tumors. The cross-scale correlation priors are beneficial for promoting the shape-aware ability for irregular tumors. Thus integrating them in a unified framework improved the multi-center breast tumor segmentation performance.

Training convolutional neural networks (CNNs) for segmentation of pulmonary airway, artery, and vein is challenging due to sparse supervisory signals caused by the severe class imbalance between tubular targets and background. We present a CNNs-based method for accurate airway and artery-vein segmentation in non-contrast computed tomography. It enjoys superior sensitivity to tenuous peripheral bronchioles, arterioles, and venules. The method first uses a feature recalibration module to make the best use of features learned from the neural networks. Spatial information of features is properly integrated to retain relative priority of activated regions, which benefits the subsequent channel-wise recalibration. Then, attention distillation module is introduced to reinforce representation learning of tubular objects. Fine-grained details in high-resolution attention maps are passing down from one layer to its previous layer recursively to enrich context. Anatomy prior of lung context map and distance transform map is designed and incorporated for better artery-vein differentiation capacity. Extensive experiments demonstrated considerable performance gains brought by these components. Compared with state-of-the-art methods, our method extracted much more branches while maintaining competitive overall segmentation performance. Codes and models are available at http://www.pami.sjtu.edu.cn/News/56.

Multispectral imaging (MSI) provides a sequence of en-face fundus spectral slices and allows for the examination of structures and signatures throughout the thickness of retina to characterize diabetic retinopathy (DR) lesions comprehensively. Manual interpretation of MSI images is commonly conducted by qualitatively analyzing both the spatial and spectral properties of multiple spectral slices. Meanwhile, there exist few computer-based algorithms that can effectively exploit the spatial and spectral information of MSI images for the diagnosis of DR. We propose a new approach that can quantify the spatial-spectral features of MSI retinal images for automatic DR lesion segmentation. It combines a generalized low-rank approximation of matrices with a supervised regularization term to generate low-dimensional spatial-spectral representations using the feature vectors in all spectral slices. Experimental results showed that the proposed approach is very effective for the segmentation of DR lesions in MSI images, which suggests it as an interesting tool for assisting ophthalmologists in diagnosing, analyzing, and managing DR lesions in MSI.

Chromosome classification is critical for karyotyping in abnormality diagnosis. To expedite the diagnosis, we present a novel method named Varifocal-Net for simultaneous classification of chromosome's type and polarity using deep convolutional networks. The approach consists of one global-scale network (G-Net) and one local-scale network (L-Net). It follows three stages. The first stage is to learn both global and local features. We extract global features and detect finer local regions via the G-Net. By proposing a varifocal mechanism, we zoom into local parts and extract local features via the L-Net. Residual learning and multi-task learning strategies are utilized to promote high-level feature extraction. The detection of discriminative local parts is fulfilled by a localization subnet of the G-Net, whose training process involves both supervised and weakly supervised learning. The second stage is to build two multi-layer perceptron classifiers that exploit features of both two scales to boost classification performance. The third stage is to introduce a dispatch strategy of assigning each chromosome to a type within each patient case, by utilizing the domain knowledge of karyotyping. The evaluation results from 1909 karyotyping cases showed that the proposed Varifocal-Net achieved the highest accuracy per patient case (%) of 99.2 for both type and polarity tasks. It outperformed state-of-the-art methods, demonstrating the effectiveness of our varifocal mechanism, multi-scale feature ensemble, and dispatch strategy. The proposed method has been applied to assist practical karyotype diagnosis.

Accurate detection of nodules in CT images is vital for lung cancer diagnosis, which greatly influences the patient's chance for survival. Motivated by successful application of convolutional neural networks (CNNs) on natural images, we propose a computer-aided diagnosis (CAD) system for simultaneous accurate pulmonary nodule detection and false positive reduction. To generate nodule candidates, we build a full 3D CNN model that employs 3D U-Net architecture as the backbone of a region proposal network (RPN). We adopt multi-task residual learning and online hard negative example mining strategy to accelerate the training process and improve the accuracy of nodule detection. Then, a 3D DenseNet-based model is presented to reduce false positive nodules. The densely connected structure reuses nodules' features and boosts feature propagation. Experimental results on LUNA16 datasets demonstrate the superior effectiveness of our approach over state-of-the-art methods.

We study the convergence of a generic half-quadratic algorithm for minimizing a wide class of $C^{1}$ objectives that occur in inverse imaging problems; this algorithm amounts to solving a sequence of positive definite systems (the inner systems) and has the advantages of simplicity and versatility. Half-quadratic optimization has been meticulously studied, both theoretically and experimentally, but two difficulties remain: first, the practical solutions of the inner systems are approximate, which may hamper convergence; and second, convergence to a stationary point of the objective is not guaranteed if the set of such points contains a continuum. We present new results that do not suffer from these limitations and hence extend our work in [M. Robini and Y. Zhu, SIAM J. Imaging Sci., 8 (2015), pp. 1752--1797]. We consider the inexact process in which the inner systems are solved to a fixed arbitrary accuracy defined in terms of the energy norm of the error. We show that this process converges to a stationary point of the objective under minimal conditions ubiquitous in regularized reconstruction and restoration. Our main results are based on the assumption that the objective has the Kurdyka--Łojasiewicz property, for which we provide constructing rules using the concept of tameness from the theory of o-minimal structures. We also propose an implementation using a truncated conjugate gradient method that controls the accuracy at negligible additional cost. Experiments on three different inverse problems show that the resulting algorithm performs well in various nonconvex scenarios and converges to solutions accurate to full machine precision.

We present new global convergence results for half-quadratic optimization in the context of image reconstruction. In particular, we do not assume that the inner optimization problem is solved exactly and we include the problematic cases where the objective function is nonconvex and has a continuum of stationary points. The inexact algorithm is modeled by a set-valued map defined from the majorization-minimization interpretation of half-quadratic optimization, and our main convergence results are based on the Kurdyka-Lojasiewicz inequality. We also propose a practical implementation that uses the conjugate gradient method and whose efficiency is illustrated by numerical experiments.

Cardiac myofibre deformation is an important determinant of the mechanical function of the heart. Quantification of myofibre strain relies on 3D measurements of ventricular wall motion interpreted with respect to the tissue microstructure. In this study, we estimated in vivo myofibre strain using 3D structural and functional atlases of the human heart. A finite element modelling framework was developed to incorporate myofibre orientations of the left ventricle (LV) extracted from 7 explanted normal human hearts imaged ex vivo with diffusion tensor magnetic resonance imaging (DTMRI) and kinematic measurements from 7 normal volunteers imaged in vivo with tagged MRI. Myofibre strain was extracted from the DTMRI and 3D strain from the tagged MRI. We investigated: i) the spatio-temporal variation of myofibre strain throughout the cardiac cycle; ii) the sensitivity of myofibre strain estimates to the variation in myofibre angle between individuals; and iii) the sensitivity of myofibre strain estimates to variations in wall motion between individuals. Our analysis results indicate that end systolic (ES) myofibre strain is approximately homogeneous throughout the entire LV, irrespective of the inter-individual variation in myofibre orientation. Additionally, inter-subject variability in myofibre orientations has greater effect on the variabilities in myofibre strain estimates than the ventricular wall motions. This study provided the first quantitative evidence of homogeneity of ES myofibre strain using minimally-invasive medical images of the human heart and demonstrated that image-based modelling framework can provide detailed insight to the mechanical behaviour of the myofibres, which may be used as a biomarker for cardiac diseases that affect cardiac mechanics.

We study the global and local convergence of a generic half-quadratic optimization algorithm inspired from the dual energy formulation of Geman and Reynolds [IEEE Trans. Pattern Anal. Mach. Intell., 14 (1992), pp. 367--383]. The target application is the minimization of $C^{1}$ convex and nonconvex objective functionals arising in regularized image reconstruction. Our global convergence proofs are based on a monotone convergence theorem of Meyer [J. Comput. System Sci., 12 (1976), pp. 108--121]. Compared to existing results, ours extend to a larger class of objectives and apply under weaker conditions; in particular, we cover the case where the set of stationary points is not discrete. Our local convergence results use a majorization-minimization interpretation to derive an insightful characterization of the basins of attraction; this new perspective grounds a formal description of the intuitive water-flooding analogy. We conclude with image restoration experiments to illustrate the efficiency of the algorithm under various nonconvex scenarios.

Free-breathing cardiac diffusion tensor imaging (DTI) is a promising but challenging technique for the study of fiber structures of the human heart in vivo. This work proposes a clinically compatible and robust technique to provide three-dimensional (3-D) fiber architecture properties of the human heart. To this end, 10 short-axis slices were acquired across the entire heart using a multiple shifted trigger delay (TD) strategy under free breathing conditions. Interscan motion was first corrected automatically using a nonrigid registration method. Then, two post-processing schemes were optimized and compared: an algorithm based on principal component analysis (PCA) filtering and temporal maximum intensity projection (TMIP), and an algorithm that uses the wavelet-based image fusion (WIF) method. The two methods were applied to the registered diffusion-weighted (DW) images to cope with intrascan motion-induced signal loss. The tensor fields were finally calculated, from which fractional anisotropy (FA), mean diffusivity (MD), and 3-D fiber tracts were derived and compared. The results show that the comparison of the FA values (FA(PCATMIP) = 0.45 ±0.10, FA(WIF) = 0.42 ±0.05, P=0.06) showed no significant difference, while the MD values ( MD(PCATMIP)=0.83 ±0.12×10(-3) mm (2)/s, MD(WIF)=0.74±0.05×10(-3) mm (2)/s, P=0.028) were significantly different. Improved helix angle variations through the myocardium wall reflecting the rotation characteristic of cardiac fibers were observed with WIF. This study demonstrates that the combination of multiple shifted TD acquisitions and dedicated post-processing makes it feasible to retrieve in vivo cardiac tractographies from free-breathing DTI acquisitions. The substantial improvements were observed using the WIF method instead of the previously published PCATMIP technique.

Idiopathic generalized epilepsy (IGE) and symptomatic generalized epilepsy (SGE) are two kinds of generalized epilepsy. In this study, we discussed the methods of automatically segmentation of MR images for patients with these two kinds of epilepsy. K-Means clustering, expectation-maximization, and fuzzy c-means algorithms were employed to perform segmentation on brain images for patients with IGE. For patients with SGE, a trimmed likelihood estimator combined with Gaussian mixture model, which we improved based on other's existing work, was employed to detect obvious brain lesions on fluid-attenuated inversion recovery images. Gray matter, white matter, and cerebrospinal fluid were then segmented from the remaining normal brain part. Similarity metrics were used to evaluate the performance of the different segmentation methods. The Dice similarity coefficient of the segmentation results exceeded 70% and satisfied the basic clinical requirement. Actually, the segmentation results were acceptable to clinicians and can provide clinicians more disease information to diagnose and treat epilepsy.

This paper studies and evaluates the feasibility and the performance of different level interpolations for improving spatial resolution of diffusion tensor magnetic resonance imaging (DT-MRI or DTI). In particular, the following techniques are investigated: anisotropic interpolation operating on scalar gray-level images, log-Euclidean interpolation method, and the quaternion interpolation method, which operate on diffusion tensor fields. The performance is evaluated both qualitatively and quantitatively using criteria such as tensor determinant, fractional anisotropy (FA), mean diffusivity (MD), fiber length, etc. We conclude that tensor field interpolations allow avoiding undesirable swelling effect in DTI, which is not the case with scalar gray-level interpolation, and that scalar gray-level image interpolation and log-Euclidean tensor field interpolation suffer from decrease in FA and MD, which may mislead the interpretation of the clinical parameters FA and MD. In contrast, the quaternion tensor field interpolation avoids such FA and MD decrease, which suggests its use for clinical applications.

This paper presents an efficient alternating direction method with patch-based dictionary updating, ADMDU-DEB, for sparse representation regularization framework of image deblurring. The main idea of the proposed method is to reformulate the variational problem as a linear equality constrained problem and then minimize its augmented Lagrangian function. The alternating direction method decouples the minimization by alternately iterating the pixel-based regularization and the patch-based sparse representation. Typically, accelerated sparse coding and simple dictionary updating applied in the sparse representation stage enable the whole algorithm to converge at a relatively small number of iterations. Additionally, the approach is readily extended to solve the same kind of variational problem with a nonnegativity constraint. Experimental results on benchmark test images consistently validate the superiority of the proposed approach and demonstrate that it achieves very competitive deblurring performance, compared with state-of-the-art deconvolution algorithms.

In recent years Bregman iterative method (or related augmented Lagrangian method) has shown to be an efficient optimization technique for various inverse problems. In this paper, we propose a two-level Bregman Method with dictionary updating for highly undersampled magnetic resonance (MR) image reconstruction. The outer-level Bregman iterative procedure enforces the sampled k-space data constraints, while the inner-level Bregman method devotes to updating dictionary and sparse representation of small overlapping image patches, emphasizing local structure adaptively. Modified sparse coding stage and simple dictionary updating stage applied in the inner minimization make the whole algorithm converge in a relatively small number of iterations, and enable accurate MR image reconstruction from highly undersampled k-space data. Experimental results on both simulated MR images and real MR data consistently demonstrate that the proposed algorithm can efficiently reconstruct MR images and present advantages over the current state-of-the-art reconstruction approach.

The use of diffusion tensor imaging (DTI) for studying the human heart in vivo is very challenging due to cardiac motion. This paper assesses the effects of cardiac motion on the human myocardial fiber architecture. To this end, a model for analyzing the effects of cardiac motion on signal intensity is presented. A Monte-Carlo simulation based on polarized light imaging data is then performed to calculate the diffusion signals obtained by the displacement of water molecules, which generate diffusion weighted (DW) images. Rician noise and in vivo motion data obtained from DENSE acquisition are added to the simulated cardiac DW images to produce motion-induced datasets. An algorithm based on principal components analysis filtering and temporal maximum intensity projection (PCATMIP) is used to compensate for motion-induced signal loss. Diffusion tensor parameters derived from motion-reduced DW images are compared to those derived from the original simulated DW images. Finally, to assess cardiac motion effects on in vivo fiber architecture, in vivo cardiac DTI data processed by PCATMIP are compared to those obtained from one trigger delay (TD) or one single phase acquisition. The results showed that cardiac motion produced overestimated fractional anisotropy and mean diffusivity as well as a narrower range of fiber angles. The combined use of shifted TD acquisitions and postprocessing based on image registration and PCATMIP effectively improved the quality of in vivo DW images and subsequently, the measurement accuracy of fiber architecture properties. This suggests new solutions to the problems associated with obtaining in vivo human myocardial fiber architecture properties in clinical conditions.

This paper proposes a sparse representation of an image using discrete delta-u functions. A delta-u function is defined as the product of a Kronecker delta function and a step function. Based on the sparse representation, we have developed a novel and effective method for reconstructing an image from limited-angle projections. The method first estimates the parameters of the sparse representation from the incomplete projection data, and then directly calculates the image to be reconstructed. Experiments have shown that the proposed method can effectively recover the missing data and reconstruct images more accurately than the total-variation (TV) regularized reconstruction method.

We propose a new fibre tracking algorithm for cardiac DT-MRI that parts with the locally ¿greedy¿ paradigm intrinsic to conventional tracking algorithms. We formulate the fibre tracking problem as the global problem of computing paths in a Boolean-weighted undirected graph. Each voxel is a vertex and edges connect every pair of neighboring voxels. We solve the underlying optimization task by Metropolis type annealing. The key features of our approach are: global optimality (unlike conventional tracking algorithms) and optimal balance between the density of fibres and the amount of available data. Besides, seed points are no longer needed; fibres are predicted in one shot for the whole DT-MRI volume without initialization artifacts.

In this paper, the multi-kernel SVM (Support Vector Machine) classification, integrated with a fusion process, is proposed to segment brain tumor from multi-sequence MRI images (T2, PD, FLAIR). The objective is to quantify the evolution of a tumor during a therapeutic treatment. As the procedure develops, a manual learning process about the tumor is carried out just on the first MRI examination. Then the follow-up on coming examinations adapts the learning automatically and delineates the tumor. Our method consists of two steps. The first one classifies the tumor region using a multi-kernel SVM which performs on multi-image sources and obtains relative multi-result. The second one ameliorates the contour of the tumor region using both the distance and the maximum likelihood measures. Our method has been tested on real patient images. The quantification evaluation proves the effectiveness of the proposed method.

Compared with other medical imaging modalities, ultrasound imaging has its own advantages. The three-dimensional (3-D) ultrasound stereo visualization technique has a broad promising future for its ability superior to traditional two-dimensional (2-D) ultrasound image, and it helps to understand the complex structures of tissues as well as to measure tissular volumes. However, it is often difficult to interpret the 3-D structure from acoustic data because of the speckle noise. To solve this problem, we propose a new enhancement algorithm which is based on calculating nonstationary degree of ultrasound data to improve the image quality. We observe data within a finite length window and then map them to an N-dimensional space where every point represents the observed data. According to the data features, we divide this space into two parts: the stationary subspace constituted by the stationary points, which represent a line in the space, and the nonstationary subspace is formed by the points out of the line. Then the nonstationary degree of a set of observed data is defined as the distance from the correspondent point to the stationary line. Thus, we can enhance the image since the nonstationary degree is larger on tissular border where features vary rapidly. Finally, the application of the proposed algorithm to real data of the liver of a rabbit is described. The results are shown by means of 3-D ultrasound stereo visualization, and the results demonstrate a significant improvement compared with the original image.

Efficient visualization of large volumetric data is a challenge for image processing community. In this paper, we present a novel volume rendering algorithm based on the concept of fractal. It consists of dividing the volumetric data set into sub-blocks, calculating the 3D fractal coefficients of each sub-block, projecting them to 2D image plane, and generating sub-images through 2D inverse fractal transform. The final rendered image is then obtained by simply summing the sub-images. Compared to the conventional ray casting technique, the proposed fractal volume rendering (FVR) method presents the advantage of reducing time complexity as well as memory complexity while maintaining good rendering quality. Moreover, the progressive refinement is supported owing to the iterative convergent process of sub-image generation

A new approach for correcting bias field in magnetic resonance (MR) images is proposed using the mathematical model of singularity function analysis (SFA), which represents a discrete signal or its spectrum as a weighted sum of singularity functions. Through this model, an MR image's low spatial frequency components corrupted by a smoothly varying bias field are first removed, and then reconstructed from its higher spatial frequency components not polluted by bias field. The thus reconstructed image is then used to estimate bias field for final image correction. The approach does not rely on the assumption that anatomical information in MR images occurs at higher spatial frequencies than bias field. The performance of this approach is evaluated using both simulated and real clinical MR images.

Radio-frequency (RF) ultrasonic data carry complete information about the object to be analyzed. Conventional analysis methods consist of exploiting only one-dimensional envelope information of the RF data, phase information being often neglected. A method is presented that is based on exploiting two-dimensional spatial phase information of RF data through the use of Gabor and Mexican hat filters. The method is illustrated with the aid of examples on physical RF data. The obtained results demonstrate the interest of spatial phase for the detection of objects in RF ultrasonic images.

A new method for the detection of textural boundaries in images is presented. The method consists of extracting texture features in the spectral domain by using the two-dimensional Wigner distribution (2D WD). A detection of the textural boundaries is readily achieved by replacing an image point by the corresponding feature parameter value calculated from the 2D WD. The algorithm is simple and can be efficiently implemented. Results are demonstrated on natural textural images.>

Several possibilities of reducing the troublesome interference terms in the Wigner distributions (WD) of 2D real signals by using different 2D analytic signals are investigated. The results show that interferences between positive and negative spatial frequencies can always be largely reduced by using a 2D analytic signal, without any loss of information, but that the use of any 2D analytic signal does not eliminate all types of interference. It is demonstrated that various kinds of interference exist and that their efficient reduction depends on the appropriate choice of different 2D analytic signals. The appropriate choice of a 2D analytic signal depends on the concrete 2D real signals spectral characteristics.>