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Salient object detection is very useful in many computer vision applications such as image segmentation, content-based image editing and object recognition. In this paper, we present a salient object detection algorithm by using color spatial distribution (CSD) and minimum spanning tree weight (MSTW). We first use a segmentation algorithm to decompose an image into superpixel-level elements, then use these elements as nodes to construct a minimum spanning tree (MST), each connected edge weight is the mean color difference between two nodes. CSD of each element can be computed by integrating color, spatial distance and MSTW. Note that if the color of one element is the most widely distributed over the entire image, it should have the biggest CSD value, we regard this element as a background node (BG Node). Then we use the MSTW between other element and BG node to generate a MSTW map. The superpixel-level saliency map can be obtained by combining the CSD map and MSTW map. Finally, we use a guided filter to get the pixel-level saliency map. Experimental results on two databases demonstrate that our proposed method outperforms other previous state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

We present a technique to recover and refine the depth map from a single image captured by a conventional camera in this paper. Our method builds on the universal imaging principle: only scene at the focus distance will converge to a single sharp point on imaging sensor but other scene will yield different blur effects varying with its distance from the camera lens. We first estimate depth values at edge locations via spectrum contrast and then recover the full depth map using a depth matting optimization method. Due to the fact that some blur textures such as soft shadows or blur patterns will produce ambiguity results during the procedure of depth estimation, we use a total variation-based image smoothing method to smooth the original image, a smoothed image with detailed texture being suppressed can be generated. Taking this smoothed image as reference image, a guided filter is used to refine the final depth map. [ABSTRACT FROM PUBLISHER]

The lown-rank tensor recovery problem is an interesting extension of thecompressed sensing. This problem consists of finding a tensor of minimumn-rank subject to linear equality constraints and has been proposed in many areas such as data mining, machine learning and computer vision. In this paper, operator splitting technique and convex relaxation technique are adapted to transform the lown-rank tensor recovery problem into a convex, unconstrained optimization problem, in which the objective function is the sum of a convex smooth function with Lipschitz continuous gradient and a convex function on a set of matrices. Furthermore, in order to solve the unconstrained nonsmooth convex optimization problem, an accelerated proximal gradient algorithm is proposed. Then, some computational techniques are used to improve the algorithm. At the end of this paper, some preliminary numerical results demonstrate the potential value and application of the tensor as well as the efficiency of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

The Nyquist–Shannon sampling theorem is on the reconstruction of a band-limited signal from its uniformly sampled samples. The higher the signal bandwidth gets, the more challenging the uniform sampling may become. To deal with this problem, signal reconstruction from local averages has been studied in the literature. In this paper, we obtain an improved Nyquist–Shannon sampling theorem from general local averages. In practice, the measurement apparatus gives a weighted average over an asymmetrical interval. As a special case, for local averages from symmetrical interval, we show that the sampling rate is much lower than that of a result by Gröchenig. Moreover, we obtain two exact dual frames from local averages, one of which improves a result by Sun and Zhou. At the end of this paper, as an example application of local average sampling, we consider a reconstruction algorithm: the piecewise linear approximations. [ABSTRACT FROM AUTHOR]

Atrial fibrillation is a most common arrhythmia. An early and accurate detection for the cure and even spread of this disease is considerably critical. The visual examination of electrocardiogram signals is the most extensively used diagnosis approach, but this method is cumbersome and low-efficient. In this work, we propose an intelligent network model based on the modified Elman neural network for signals discrimination. Motivated from the exponential moving average strategy, the proposed model is capable of fully modeling the information feedback and also effectively and efficiently striking a balance between current information representation and historical information representation in original Elman neural network. To evaluate its practicability, the model is also plugged into a convolutional neural network framework and two control subjects are established for a fair comparison. Experiments on the MIT-BIH atrial fibrillation and arrhythmia databases show that the proposed model can enjoy a consistent improvement in classification performance with the accuracy of 98.2% and 97.2% respectively and exhibit lower convergence rate than existing Elman network. Thanks to its high model performance, we are planning to develop the model into a computer-aided diagnosis system to assist physicians. • We design modified Elman network (MENN) for atrial fibrillation (AF) detection. • Patient-independent validation ensures the model robustness. • The feature extraction and classification are not required. • To our knowledge, this is the first time to redesign ENN for AF detection. [ABSTRACT FROM AUTHOR]

Robust principal component analysis (RPCA) has recently seen ubiquitous activity for dimensionality reduction in image processing, visualization and pattern recognition. Conventional RPCA methods model the low-rank component as regularizing each singular value equally. However, in numerous modern applications, each singular value has different physical meaning and should be treated differently. This is one of the main reasons why RPCA techniques cannot work well in dealing with many realistic problems. To solve this problem, a novel hierarchical Bayesian RPCA model with adaptive singular value penalty is proposed. This model enforces the low-rank constraint by introducing an adaptive penalty function on the singular values of the low-rank component. In particular, we impose a hierarchical Exponent-Gamma prior on the singular values of the low-rank component and the Beta-Bernoulli prior on sparsity indicators. The variational Bayesian framework and the Markov chain Monte Carlo-based Bayesian inference are considered for inferring the posteriors of all latent variables involved in low-rank and sparse components. Numerical experiments demonstrate the competitive performance of the proposed model on synthetic and real data. [ABSTRACT FROM AUTHOR]

Thresholding based iterative algorithms have the trade-off between effectiveness and optimality. Some are effective but involving sub-matrix inversions in every step of iterations. For systems of large sizes, such algorithms can be computationally expensive and/or prohibitive. The null space tuning algorithm with hard thresholding and feedbacks (NST+HT+FB) has a mean to expedite its procedure by a suboptimal feedback, in which sub-matrix inversion is replaced by an eigenvalue-based approximation. The resulting suboptimal feedback scheme becomes exceedingly effective for large system recovery problems. An adaptive algorithm based on thresholding, suboptimal feedback and null space tuning (AdptNST+HT+subOptFB) without a prior knowledge of the sparsity level is also proposed and analyzed. Convergence analysis is the focus of this article. [ABSTRACT FROM AUTHOR]

Presents an equivalent theorem for linear combinations of Gamma operators. Ditzian-Totik moduli of smoothness; Theorems, lemmas and proofs.

This paper develops a new frame for non-stationary signal separation, which is a combination of wavelet transform, clustering strategy and local maximum approximation. We provide a rigorous mathematical theoretical analysis and prove that the proposed algorithm can estimate instantaneous frequencies and sub-signal modes from a blind source signal. The error bounds for instantaneous frequency estimation and sub-signal recovery are provided. Numerical experiments on synthetic and real data demonstrate the effectiveness and efficiency of the proposed algorithm. Our method based on wavelet transform can be extended to other time-frequency transforms, which provides a new perspective of time-frequency analysis tools in solving the non-stationary signal separation problem.

Since magnetic resonance imaging (MRI) has superior soft tissue contrast, contouring (brain) tumor accurately by MRI images is essential in medical image processing. Segmenting tumor accurately is immensely challenging, since tumor and normal tissues are often inextricably intertwined in the brain. It is also extremely time consuming manually. Late deep learning techniques start to show reasonable success in brain tumor segmentation automatically. The purpose of this study is to develop a new region-of-interest-aided (ROI-aided) deep learning technique for automatic brain tumor MRI segmentation. The method consists of two major steps. Step one is to use a 2D network with U-Net architecture to localize the tumor ROI, which is to reduce the impact of normal tissue's disturbance. Then a 3D U-Net is performed in step 2 for tumor segmentation within identified ROI. The proposed method is validated on MICCAI BraTS 2015 Challenge with 220 high Gliomas grade (HGG) and 54 low Gliomas grade (LGG) patients' data. The Dice similarity coefficient and the Hausdorff distance between the manual tumor contour and that segmented by the proposed method are 0.876 ±0.068 and 3.594±1.347 mm, respectively. These numbers are indications that our proposed method is an effective ROI-aided deep learning strategy for brain MRI tumor segmentation, and a valid and useful tool in medical image processing., Competing Interests: Conflict of interestThe authors declare that they have no conflicts of interest., (© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022.)