Strong Multiplicative Noise Research Articles

ViT-DexiNet: a vision transformer-based edge detection operator for small object detection in SAR images

ABSTRACTThis paper introduces a novel edge detection operator called ‘vision transformer-based Dexinet (ViT-DexiNet)’ to address the challenges of detecting small objects in synthetic aperture radar (SAR) images. SAR images are typically impacted by strong multiplicative noise, making edge detection difficult. Existing traditional methods have limited spectral data preservation capabilities and often result in a loss of clarity and integrity of salient features in SAR images. The proposed ViT-DexiNet operator employs a series of interconnected layers to extract and refine salient edge features from SAR images. It utilizes a vision transformer self-attention layer to capture the pattern and structural details of image features crucial for determining edges. The extracted feature maps are then processed by the DexiNet architecture, which consists of a dense block, transfer block, and upsampling network. This architecture helps preserve edge information at different scales in deeper layers. The series of layered blocks generate edge maps, which are concatenated and averaged through smoothing to remove noise and enhance edge details in SAR images, resulting in a final high-quality edge map. To evaluate the proposed ViT-DexiNet method, both qualitative and quantitative analyses are conducted using standard edge detection operators such as Canny and Sobel. The empirical results demonstrate that the ViT-DexiNet surpasses baseline edge detection operators. The achieved values of proposed edge detection operator are 97.92%, 97.72%, 97.64% and 97.41%, respectively for the metrics accuracy, precision, recall and f1-score. The ViT-DexiNet offers high-quality edge maps, simplifying the interpretation of data for small object detection. Overall, the ViT-DexiNet method shows promise in overcoming the limitations of traditional approaches and improving the detection of edges in SAR images.

Random invariant manifolds and foliations for slow-fast PDEs with strong multiplicative noise

This article is devoted to the dynamical behaviors of a class of slow-fast PDEs perturbed by strong multiplicative noise. We will accomplish the existence of random invariant manifolds and foliations, and show exponential tracking property of them. Moreover, the asymptotic approximation for both objects will be presented.

Training CNNs on speckled optical dataset for edge detection in SAR images

Edge detection in SAR images is a difficult task due to the strong multiplicative noise. Many researches have been dedicated to edge detection in SAR images but very few try to address the most challenging 1-look situations. Motivated by the success of CNNs for the analysis of natural images, we develop a CNN edge detector for 1-look SAR images. We propose to simulate a SAR dataset using the optical dataset BSDS500 to avoid the tedious job of edge labeling, and we propose a framework, a hand-crafted layer followed by learnable layers, to enable the model trained on simulated SAR images to work in real SAR images. The hypothesis behind these two propositions is that both optical and SAR images can be divided into piecewise constant areas and edges are boundaries between two homogeneous areas. The hand-crafted layer, which is defined by a ratio based gradient computation method, helps to tackle the gap between training and testing images, because the gradient distribution will not be influenced by the mean intensity values of homogeneous areas. The gradient computation step is done by Gradient by Ratio (GR) and the learnable layers are identical to those in HED. The proposed edge detector, GRHED, outperforms concurrent approaches in all our simulations especially in two 1-look real SAR images.

Factorization-Based Active Contour for Water-Land SAR Image Segmentation via the Fusion of Features

The segmentation of synthetic aperture radar (SAR) water-land images is a very difficult task not only because of strong multiplicative noise but also due to the blurred boundary, irregular shape, and together with diminished contrast. In this paper, we propose a matrix factorization active contour model based on fused features for SAR image segmentation. First, to enhance the robustness, multiple features are utilized. For each pixel location, feature maps (matrix) are constructed by combining wavelet textual features, Gaussian (DoG) filter features, and Gabor filter features via local spectral histogram, which improves spatial pattern and express image structure. Second, the energy function is constructed based on region information and edge information of SAR image. Region information is obtained via matrix factorization theory on the feature matrix. Edge information is obtained by modified the ratio of exponentially weighted averages operator. Then, a convex energy function is proposed to avoid the local minima. A fast dual formulation is introduced for the evolution of the contour. Finally, synthetic and real SAR data are used for verification. The experimental results demonstrate the proposed algorithm is effective for water/land segmentation in SAR images.

A Multi-Region Segmentation Method for SAR Images based on the Multi-Texture Model with Level Sets.

Synthetic Aperture Radar (SAR) image segmentation is a difficult problem due to the presence of strong multiplicative noise. To attain multi-region segmentation for SAR images, this paper presents a parametric segmentation method based on the multi-texture model with level sets. Segmentation is achieved by solving level set functions obtained from minimizing the proposed energy functional. To fully utilize image information, edge feature and region information are both included in the energy functional. For the need of level set evolution, the Ratio of Exponentially Weighted Averages (ROEWA) operator is modified to obtain edge feature. Region information is obtained by the Improved Edgeworth Series Expansion (IESE), which can adaptively model a SAR image distribution with respect to various kinds of regions. The performance of the proposed method is verified by three high resolution SAR images. The experimental results demonstrate that SAR images can be segmented into multiple regions accurately without any speckle pre-processing steps by the proposed method.

Multiplicative noise induces zero critical frequency

Stochastic Bloch equations which model the fluorescence of two-level molecules and atoms, NMR experiments, and Josephson junctions are investigated to illustrate the profound effect of multiplicative noise on the critical frequency of a dynamical system. Using exact solutions and the cumulant expansion we find two main effects: (i) even very weak noise may double or triple the number of critical frequencies, which is related to an instability of the system, and (ii) strong multiplicative noise may induce a nontrivial zero critical frequency thus wiping out the overdamped phase.

SAR Image Segmentation Based on Level Set With Stationary Global Minimum

In this letter, we propose a new level-set-based energy functional for the purpose of synthetic aperture radar (SAR) image segmentation into Gamma homogeneous regions. The segmentation of SAR images is a difficult problem due to the presence of speckles, which can be modeled as strong multiplicative noise. Our proposed energy functional is designed to get a stationary global minimum. As a result, the level set function that evolves by the Euler-Lagrange equation of the energy functional has a unique stationary convergence state. Moreover, it is easy to set a termination criterion on the curve evolution via a level set by using our energy functional. The experimental results on both synthetic and real SAR images demonstrate the effectiveness of our method.

Robust Shape Tracking With Multiple Models in Ultrasound Images

This paper addresses object tracking in ultrasound images using a robust multiple model tracker. The proposed tracker has the following features: 1) it uses multiple dynamic models to track the evolution of the object boundary, and 2) it models invalid observations (outliers), reducing their influence on the shape estimates. The problem considered in this paper is the tracking of the left ventricle which is known to be a challenging problem. The heart motion presents two phases (diastole and systole) with different dynamics, the multiple models used in this tracker try to solve this difficulty. In addition, ultrasound images are corrupted by strong multiplicative noise which prevents the use of standard deformable models. Robust estimation techniques are used to address this difficulty. The multiple model data association (MMDA) tracker proposed in this paper is based on a bank of nonlinear filters, organized in a tree structure. The algorithm determines which model is active at each instant of time and updates its state by propagating the probability distribution, using robust estimation techniques.

Hypersensitive transport in a phase model with multiplicative stimulus

In a simple system with periodic symmetric potential, the phase model under effect of strong multiplicative noise or periodic square wave, we found a giant response, in the form of directed flux, to an ultrasmall dc signal. The resulting flux demonstrates a bell-shaped dependence on multiplicative noise correlation time and occurs even in the case of large (compared to the signal) additive noise.

Unbiased estimate of forces from measured correlation functions, including the case of strong multiplicative noise

Starting from appropriate short-time correlation function measurements, we propose a dynamical “learning” method to derive the deterministic and stochastic forces underlying an observed process, even if this process contains strong multiplicative noise. To do this we extend the ideas of our previous paper [1] to establish mathematical relationships in this more general case between the joint distribution function of the process and its corresponding Ito-Langevin equation. A numerical example for a simulated process containing strong multiplicative noise shows good agreement with the theory.