A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Integrating IoT and Novel Approaches to Enhance Electromagnetic Image Quality using Modern Anisotropic Diffusion and Speckle Noise Reduction Techniques

Electromagnetic imaging is becoming more important in many sectors, and this requires high-quality pictures for reliable analysis. This study makes use of the complementary relationship between IoT and current image processing methods to improve the quality of electromagnetic images. The research presents a new framework for connecting Internet of Things sensors to imaging equipment, allowing for instantaneous input and adjustment. At the same time, the suggested system makes use of sophisticated anisotropic diffusion algorithms to bring out key details and hide noise in electromagnetic pictures. In addition, a cutting-edge technique for reducing speckle noise is used to combat this persistent issue in electromagnetic imaging. The effectiveness of the suggested system was determined via a comparison to standard imaging techniques. There was a noticeable improvement in visual sharpness, contrast, and overall clarity without any loss of information, as shown by the results. Incorporating IoT sensors also facilitated faster calibration and real-time modifications, which opened up new possibilities for use in contexts with a high degree of variation. In fields where electromagnetic imaging plays a crucial role, such as medicine, remote sensing, and aerospace, the ramifications of this study are far-reaching. Our research demonstrates how the Internet of Things (IoT) and cutting-edge image processing have the potential to dramatically improve the functionality and versatility of electromagnetic imaging systems

Edge-enhancing Filters with Negative Weights

In [DOI:10.1109/ICMEW.2014.6890711], a graph-based denoising is performed by projecting the noisy image to a lower dimensional Krylov subspace of the graph Laplacian, constructed using nonnegative weights determined by distances between image data corresponding to image pixels. We~extend the construction of the graph Laplacian to the case, where some graph weights can be negative. Removing the positivity constraint provides a more accurate inference of a graph model behind the data, and thus can improve quality of filters for graph-based signal processing, e.g., denoising, compared to the standard construction, without affecting the costs.Comment: 5 pages; 6 figures. Accepted to IEEE GlobalSIP 2015 conferenc

Segmentation of ultrasound images of thyroid nodule for assisting fine needle aspiration cytology

The incidence of thyroid nodule is very high and generally increases with the age. Thyroid nodule may presage the emergence of thyroid cancer. The thyroid nodule can be completely cured if detected early. Fine needle aspiration cytology is a recognized early diagnosis method of thyroid nodule. There are still some limitations in the fine needle aspiration cytology, and the ultrasound diagnosis of thyroid nodule has become the first choice for auxiliary examination of thyroid nodular disease. If we could combine medical imaging technology and fine needle aspiration cytology, the diagnostic rate of thyroid nodule would be improved significantly. The properties of ultrasound will degrade the image quality, which makes it difficult to recognize the edges for physicians. Image segmentation technique based on graph theory has become a research hotspot at present. Normalized cut (Ncut) is a representative one, which is suitable for segmentation of feature parts of medical image. However, how to solve the normalized cut has become a problem, which needs large memory capacity and heavy calculation of weight matrix. It always generates over segmentation or less segmentation which leads to inaccurate in the segmentation. The speckle noise in B ultrasound image of thyroid tumor makes the quality of the image deteriorate. In the light of this characteristic, we combine the anisotropic diffusion model with the normalized cut in this paper. After the enhancement of anisotropic diffusion model, it removes the noise in the B ultrasound image while preserves the important edges and local details. This reduces the amount of computation in constructing the weight matrix of the improved normalized cut and improves the accuracy of the final segmentation results. The feasibility of the method is proved by the experimental results.Comment: 15pages,13figure