Data Fitting Term Research Articles

An active contour model algorithm combined with anisotropic diffusion filtering and global pre-fitting energy

Traditional local active contour models mainly depend on the data fitting term to obtain image edge information, which are sensitive to the position of initial contour. In fact, setting an unreasonable initial contour will result in a time-consuming image segmentation process and difficult evolution at weak boundary. To solve this problem, we come up with a second-order edge detection operator which is based on the global gradient image information to replace the traditional data fitting term, and to obtain edge information with higher speed and accuracy. In addition, the anisotropic edge enhancement method has been introduced to improve the robustness to the weak boundary. In this way, an active contour model which is insensitive to initial contour position is proposed to achieve a faster and more accurate image segmentation result.

Improved Hybrid Particle Swarm Optimizer with Sine-Cosine Acceleration Coefficients for Transient Electromagnetic Inversion

Background: Recently, Particle Swarm Optimization (PSO) has been increasingly used in geophysics due to its simple operation and fast convergence. Objective: However, PSO lacks population diversity and may fall to local optima. Hence, an Improved Hybrid Particle Swarm Optimizer with Sine-Cosine Acceleration Coefficients (IH-PSO-SCAC) is proposed and successfully applied to test functions in Transient Electromagnetic (TEM) nonlinear inversion. Method: A reverse learning strategy is applied to optimize population initialization. The sine-cosine acceleration coefficients are utilized for global convergence. Sine mapping is adopted to enhance population diversity during the search process. In addition, the mutation method is used to reduce the probability of premature convergence. Results: The application of IH-PSO-SCAC in the test functions and several simple layered models are demonstrated with satisfactory results in terms of data fit. Two inversions have been carried out to test our algorithm. The first model contains an underground low-resistivity anomaly body and the second model utilized measured data from a profile of the Xishan landslide in Sichuan Province. In both cases, resistivity profiles are obtained, and the inverse problem is solved for verification. Conclusion: The results show that the IH-PSO-SCAC algorithm is practical, can be effectively applied in TEM inversion and is superior to other representative algorithms in terms of stability and accuracy.

Generalized Functional Pruning Optimal Partitioning (GFPOP) for Constrained Changepoint Detection in Genomic Data

We describe a new algorithm and R package for peak detection in genomic data sets using constrained changepoint models. These detect changes from background to peak regions by imposing the constraint that the mean should alternately increase then decrease. An existing algorithm for this problem exists, and gives state-of-the-art accuracy results, but it is computationally expensive when the number of changes is large. We propose a dynamic programming algorithm that jointly estimates the number of peaks and their locations by minimizing a cost function which consists of a data fitting term and a penalty for each changepoint. Empirically this algorithm has a cost that is O(N log(N )) for analyzing data of length N . We also propose a sequential search algorithm that finds the best solution with K segments in O(log(K) N log(N )) time, which is much faster than the previous O(K N log(N )) algorithm. We show that our disk-based implementation in the PeakSegDisk R package can be used to quickly compute constrained optimal models with many changepoints, which are needed to analyze typical genomic data sets that have tens of millions of observations.

ADMM-ADAM: A New Inverse Imaging Framework Blending the Advantages of Convex Optimization and Deep Learning

Alternating direction method of multipliers (ADMM) and adaptive moment estimation (ADAM) are two optimizers of paramount importance in convex optimization (CO) and deep learning (DL), respectively. Numerous state-of-the-art algorithms for solving inverse problems are achieved by carefully designing a convex criterion, typically composed of a data-fitting term and a regularizer. Even when the regularizer is convex, its mathematical form is often sophisticated, hence inducing a math-heavy optimization procedure and making the algorithm design a daunting task for software engineers. Probably for this reason, people turn to solve the inverse problems via DL, but this requires big data collection, quite time-consuming if not impossible. Motivated by these facts, we propose a new framework, termed as ADMM-ADAM, for solving inverse problems. As the key contribution, even just with small/single data, the proposed ADMM-ADAM is able to exploit DL to obtain a convex regularizer of very simple math form, followed by solving the regularized criterion using simple CO algorithm. As a side contribution, a state-of-the-art hyperspectral inpainting algorithm is designed under ADMM-ADAM, demonstrating its superiority even without the aid of big data or sophisticated mathematical regularization.

A variational non-linear constrained model for the inversion of FDEM data* *Dedicated to Lothar Reichel on the occasion of his 70th birthday.

Reconstructing the structure of the soil using non-invasive techniques is a very relevant problem in many scientific fields, like geophysics and archaeology. This can be done, for instance, with the aid of frequency domain electromagnetic (FDEM) induction devices. Inverting FDEM data is a very challenging inverse problem, as the problem is extremely ill-posed, i.e. sensible to the presence of noise in the measured data, and non-linear. Regularization methods substitute the original ill-posed problem with a well-posed one whose solution is an accurate approximation of the desired one. In this paper we develop a regularization method to invert FDEM data. We propose to determine the electrical conductivity of the ground by solving a variational problem. The minimized functional is made up by the sum of two term: the data fitting term ensures that the recovered solution fits the measured data, while the regularization term enforces sparsity on the Laplacian of the solution. The trade-off between the two terms is determined by the regularization parameter. This is achieved by minimizing an ℓ 2 − ℓ q functional with 0 < q ⩽ 2. Since the functional we wish to minimize is non-convex, we show that the variational problem admits a solution. Moreover, we prove that, if the regularization parameter is tuned accordingly to the amount of noise present in the data, this model induces a regularization method. Some selected numerical examples on synthetic and real data show the good performances of our proposal.

A LogTVSCAD Nonconvex Regularization Model for Image Deblurring in the Presence of Impulse Noise

This paper proposes a nonconvex model (called LogTVSCAD) for deblurring images with impulsive noises, using the log-function penalty as the regularizer and adopting the smoothly clipped absolute deviation (SCAD) function as the data-fitting term. The proposed nonconvex model can effectively overcome the poor performance of the classical TVL1 model for high-level impulsive noise. A difference of convex functions algorithm (DCA) is proposed to solve the nonconvex model. For the model subproblem, we consider the alternating direction method of multipliers (ADMM) algorithm to solve it. The global convergence is discussed based on Kurdyka–Lojasiewicz. Experimental results show the advantages of the proposed nonconvex model over existing models.

A neighbor level set framework minimized with the split Bregman method for medical image segmentation

Medical image segmentation has a huge challenge due to intensity inhomogeneity and the similarity of the background and the object. To meet this challenge, we propose an improved active contour model, in which we combine the level set method and the split Bregman method, and provide the two-phase formulation, the multi-phase formulation and 3D formulation. In this paper, the proposed model is presented in a level set framework by including the neighbor region information for segmenting medical images in which the energy functional contains the data fitting term and the length term. The neighbor region and the local intensity variances in the data fitting term are designed to optimize the minimization process. To minimize the energy functional then we apply the split Bregman method which contributes to get faster convergence. Besides, we extend our model to the multi-phase segmentation model and the 3D segmentation model for cardiac MR images, which have all achieved good results. Experimental results show that the new model not only has strong robustness to other cardiac tissue effects and image intensity inhomogeneity, but it also can much better conduce to the extraction of effective tissues. As we expected, our model has higher segmentation accuracy and efficiency for medical image segmentation.

High quality 3D reconstruction based on fusion of polarization imaging and binocular stereo vision

Polarization imaging can retrieve inaccurate objects’ 3D shapes with fine textures, whereas coarse but accurate depths can be provided by binocular stereo vision. To take full advantage of these two complementary techniques, we investigate a novel 3D reconstruction method based on the fusion of polarization imaging and binocular stereo vision for high quality 3D reconstruction. We first generate the polarization surface by correcting the azimuth angle errors on the basis of registered binocular depth, to solve the azimuthal ambiguity in the polarization imaging. Then we propose a joint 3D reconstruction model for depth fusion, including a data fitting term and a robust low-rank matrix factorization constraint. The former is to transfer textures from the polarization surface to the fused depth by assuming their relationship linear, whereas the latter is to utilize the low-frequency part of binocular depth to improve the accuracy of the fused depth considering the influences of missing-entries and outliers. To solve the optimization problem in the proposed model, we adopt an efficient solution based on the alternating direction method of multipliers. Extensive experiments have been conducted to demonstrate the efficiency of the proposed method in comparison with state-of-the-art methods and to exhibit its wide application prospects in 3D reconstruction.

Instance segmentation of fallen trees in aerial color infrared imagery using active multi-contour evolution with fully convolutional network-based intensity priors

Over the last several years, semantic image segmentation based on deep neural networks has been greatly advanced. On the other hand, single-instance segmentation still remains a challenging problem. In this paper, we introduce a framework for segmenting instances of a common object class by multiple active contour evolution over semantic segmentation maps of images obtained through fully convolutional networks. The contour evolution is cast as an energy minimization problem, where the aggregate energy functional incorporates a data fit term, an explicit shape model, and accounts for object overlap. Efficient solution neighborhood operators are proposed, enabling optimization through metaheuristics such as simulated annealing. We instantiate the proposed framework in the context of segmenting individual fallen stems from high-resolution aerial multispectral imagery, providing problem-specific energy potentials. We validated our approach on 3 real-world scenes of varying complexity, using 730 manually labeled polygon outlines as ground truth. The test plots were situated in regions of the Bavarian Forest National Park, Germany, which sustained a heavy bark beetle infestation. Evaluations were performed on both the polygon and line segment level, showing that the multi-contour segmentation can achieve up to 0.93 precision and 0.82 recall. An improvement of up to 7 percentage points (pp) in recall and 6 in precision compared to an iterative sample consensus line segment detection baseline was achieved. Despite the simplicity of the applied shape parametrization, an explicit shape model incorporated into the energy function improved the results by up to 4 pp of recall. Finally, we show the importance of using a high-quality semantic segmentation method (e.g. U-net) as the basis for individual stem detection, as the quality of the results degraded dramatically in our baseline experiment utilizing a simpler method. Our method is a step towards increased accessibility of automatic fallen tree mapping in forests, due to higher cost efficiency of aerial imagery acquisition compared to laser scanning. The precise fallen tree maps could be further used as a basis for plant and animal habitat modeling, studies on carbon sequestration as well as soil quality in forest ecosystems.

Beyond universals and particulars in language

In his target article “General linguistics must be based on universals (or nonconventional aspects of language)”, Martin Haspelmath invites us to reconsider the distinction between general linguistics and the linguistics of a particular language. The distinction is clearly useful to demarcate foci of interest and job descriptions. Also, it helps clarify what we expect our theories and models to achieve in terms of data fit: In general linguistics, we expect theories and models to capture something about the general nature of language. Now, since we can test the relevant hypotheses only in a relatively small sample of currently known languages, we want to avoid what statisticians call overfitting our particular sample. This means that we don’t expect models to perfectly fit every single language in this one sample; instead, we expect models to have good predictive performance in any sample we choose, allowing for random historical fluctuations and a healthy modicum of uncertainty. From a language-particular study, by contrast, we expect theories and models to capture one specific language, from its most general regularities to its most specific exceptions. We can’t overfit at that level. Where we do want to avoid overfitting is at the level of the idiosyncrasies that characterize individual speakers/signers or individual utterances (or, say, individual glyph tokens when we want to generalize not over an entire language but only over its inscriptional record). Beyond clarifying these differences, I don’t think the distinction between general and particular linguistics takes us much further. In important respects the two enterprises are heavily intertwined: Language-particular findings can generate hypotheses about the general nature of language (e.g. the discovery of free affix order in one language led to a learning-based hypothesis why most avoid it: Mansfield et al. 2020), and general linguistics obviously depends on samples of language-particular analyses. Haspelmath proposes that the distinction take us further nevertheless. The proposal rests on linking the distinction to two demands: general linguistics (1) “must study universals”, and (2) needs “comparative concepts” that are independent of the categories we need for describing particular languages. I am not convinced that these two demands are helpful.

Directional TGV-Based Image Restoration under Poisson Noise.

We are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or glass fibres. In order to deal with these problems, the Directional Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and 2019, in the case of impulse and Gaussian noise. In this article we focus on images corrupted by Poisson noise, extending the DTGV regularization to image restoration models where the data fitting term is the generalized Kullback–Leibler divergence. We also propose a technique for the identification of the main texture direction, which improves upon the techniques used in the aforementioned work about DTGV. We solve the problem by an ADMM algorithm with proven convergence and subproblems that can be solved exactly at a low computational cost. Numerical results on both phantom and real images demonstrate the effectiveness of our approach.

A fast algorithm for group square-root Lasso based group-sparse regression

Group square-root Lasso (GSRL) is a promising tool for group-sparse regression since the hyperparameter is independent of noise level. Recent works also reveal its connections to some statistically sound and hyperparameter-free methods, e.g., group-sparse iterative covariance-based estimation (GSPICE). However, the non-smoothness of the data-fitting term leads to the difficulty in solving the optimization problem of GSRL, and available solvers usually suffer either slow convergence or restrictions on the dictionary. In this paper, we propose a class of efficient solvers for GSRL in a block coordinate descent manner, including group-wise cyclic minimization (GCM) for group-wise orthonormal dictionary and generalized GCM (G-GCM) for general dictionary. Both strict descent property and global convergence are proved. To cope with signal processing applications, the complex-valued multiple measurement vectors (MMV) case is considered. The proposed algorithm can also be used for the fast implementation of methods with theoretical equivalence to GSRL, e.g., GSPICE. Significant superiority in computational efficiency is verified by simulation results.

2DNMR data inversion using locally adapted multi-penalty regularization

Geologists and Reservoir Engineers routinely use time-domain nuclear magnetic resonance (NMR) to learn about the porous structure of rocks that hold underground fluids. In particular, two-dimensional NMR (2DNMR) technique is now gaining importance in a wide variety of applications. Crucial issue in 2DNMR analysis are the speed, robustness and accuracy of the data inversion process. This paper proposes a multi-penalty method with locally adapted regularization parameters for fast and accurate inversion of 2DNMR data. The method solves an unconstrained optimization problem whose objective function contains a data-fitting term, a single L1 penalty parameter and a multiple parameter L2 penalty. We propose an adaptation of the Fast Iterative Shrinkage and Thresholding (FISTA) method to solve the multi-penalty minimization problem, and an automatic procedure to compute all the penalty parameters. This procedure generalizes the Uniform Penalty principle introduced in [Bortolotti et al., Inverse Problems, 33(1), 2016]. The proposed approach allows us to obtain accurate 2D relaxation time distributions while keeping short the computation time. Results of numerical experiments on synthetic and real data prove that the proposed method is efficient and effective in reconstructing the peaks and the flat regions that usually characterize 2DNMR relaxation time distributions.

Adaptive segmentation model for liver CT images based on neural network and level set method

Accurate segmentation is difficult for liver computed tomography (CT) images, since the liver CT images do not always have obvious and smooth boundaries. The location of the tumor is not specified and the image intensity is similar to that of the liver. Although manual and automatic segmentation methods, traditional and deep learning models currently exist, none can be specifically and effectively applied to segment liver CT images. In this paper, we propose a new model based on a level set framework for liver CT images in which the energy functional contains three terms including the data fitting term, the length term and the bound term. Then we apply the split Bregman method to minimize the energy functional that leads the energy functional to converge faster. The proposed model is robust to initial contours and can segment liver CT images with intensity inhomogeneity and unclear boundaries. In the bound term, we use the U-Net to get constraint information which has a considerable influence on effective and accurate segmentation. We improve a multi-phase level set of our model to get contours of tumor and liver at the same time. Finally, a parallel algorithm is proposed to improve segmentation efficiency. Results and comparisons of experiments are shown to demonstrate the merits of the proposed model including robustness, accuracy, efficiency and intelligence.

On Two Algorithms for Multi-Modality Image Registration Based on Gaussian Curvature and Application to Medical Images

Registration of multi-modal images is one of the challenging problems in image processing nowadays. In this paper, two novel non-rigid registration models are proposed for multi-modality images. In model 1, mutual information of the template and reference images is used as data fitting term with Gaussian curvature regularization. This approach may not give satisfactory results in noisy images or images having bias field. To overcome this drawback, model 2 is proposed which is based on normalized gradient of both template and reference images as a data fitting term instead of mutual information. To get best transformations, both the models are minimized by using Augmented Lagrangian Method. The proposed models can register multi-modality images without effecting edges and other important fine details and are also tested on various medical images like (T1-T2 MRI, PD weighted-T2 MRI) noisy and synthetic images. The proposed models are also tested on a well known free available Brainweb dataset, where they produced satisfactory results. From experimental results, it can be observed that normalized gradient field based model gives better results than mutual information based model. Comparison is done qualitatively and quantitatively through Jaccard Similarity Coefficient.

Low Rank Tensor Completion With Poisson Observations.

Poisson observations for videos are important models in video processing and computer vision. In this paper, we study the third-order tensor completion problem with Poisson observations. The main aim is to recover a tensor based on a small number of its Poisson observation entries. A existing matrix-based method may be applied to this problem via the matricized version of the tensor. However, this method does not leverage on the global low-rankness of a tensor and may be substantially suboptimal. Our approach is to consider the maximum likelihood estimate of the Poisson distribution, and utilize the Kullback-Leibler divergence for the data-fitting term to measure the observations and the underlying tensor. Moreover, we propose to employ a transformed tensor nuclear norm ball constraint and a bounded constraint of each entry, where the transformed tensor nuclear norm is used to get a lower transformed multi-rank tensor with suitable unitary transformation matrices. We show that the upper bound of the error of the estimator of the proposed model is less than that of the existing matrix-based method. Also an information theoretic lower error bound is established. An alternating direction method of multipliers is developed to solve the resulting convex optimization model. Extensive numerical experiments on synthetic data and real-world datasets are presented to demonstrate the effectiveness of our proposed model compared with existing tensor completion methods.

Sparse signal reconstruction for nonlinear models via piecewise rational optimization

We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and a penalization term. In contrast with most previous works which settle for approximated local solutions, we seek for a global solution to the obtained challenging nonconvex problem. Our global approach relies on the so-called Lasserre relaxation of polynomial optimization.We here specifically include in our approach the case of piecewise rational functions, which makes it possible to address a wide class of nonconvex exact and continuous relaxations of the ℓ0 penalization function. Additionally, we study the complexity of the optimization problem. It is shown how to use the structure of the problem to lighten the computational burden efficiently. Finally, numerical simulations illustrate the benefits of our method in terms of both global optimality and signal reconstruction.

SAR Image Despeckling Employing a Recursive Deep CNN Prior

Synthetic aperture radar (SAR) images are inherently affected by speckle noise, for which deep learning-based methods have shown good potential. However, the deep learning-based methods proposed until now directly map low-quality images to high-quality images, and they are unable to characterize the priors for all the kinds of speckle images. The variational method is a classic model optimization approach that establishes the relationship between the clean and noisy images from the perspective of a probability distribution. Therefore, in this article, we propose the recursive deep convolutional neural network (CNN) prior model for SAR image despeckling (SAR-RDCP). First, the data-fitting term and regularization term of the SAR variational model are decoupled into two subproblems, i.e., a data-fitting block and a deep CNN prior block. The gradient descent algorithm is then used to solve the data-fitting block, and a predenoising residual channel attention network based on dilated convolution is used for the deep CNN prior block, which combines an end-to-end iterative optimization training. In the experiments undertaken in this study, the proposed model was compared with several state-of-the-art despeckling methods, obtaining better results in both the quantitative and qualitative evaluations.

A TV-log nonconvex approach for image deblurring with impulsive noise

In this paper, we study the image deblurring with impulsive noise problem. In order to find a high quality recovery solution, we propose a nonconvex optimization model that combines total variation regularization and nonconvex log penalty for data fitting. The new model can overcome the limitation of the L1-norm penalized data fitting term with total variation regularization model for high noise levels, and is easier to choose the scalar parameter in the data fitting term than the existing methods. For solving the nonconvex optimization problem, a difference of convex (DC) functions algorithm with adaptive proximal parameter is developed. Theoretically, using the Kurdyka-Łojasiewicz property, we establish that the sequence generated by the proposed algorithm converges to a critical point. The experiment results demonstrate the superiority of the new approach against the competing methods.

A nonconvex [formula omitted] model for image restoration with impulse noise

In this paper, we propose a model for image restoration with blur and impulse noise, it is composed of l1 data fitting term and a nonconvex regularization term, which is the weighted difference of l1-norm and l2-norm based on wavelet frame. The combined model is difficult to solve by the corresponding Euler Lagrangian equations, here we solve it by alternating direction method of multipliers (ADMM). We describe the detailed process of the algorithm, and establish the convergence of the algorithm. The experimental outcomes on different blurs and different impulse noises demonstrate that the proposed approach is better than those existing methods in terms of standard signal-to-noise ratio (PSNR), relative error (ReErr), and visual quality.