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Optical flow is the pattern of apparent motion of objects in a scene. The computation of optical flow is a critical component in numerous computer vision tasks such as object detection, visual object tracking, and activity recognition. Despite a lot of research, efficiently managing abrupt changes in motion remains a challenge in motion estimation. This paper proposes novel variational regularization methods to address this problem since they allow combining different mathematical concepts into a joint energy minimization framework. In this work, we incorporate concepts from signal sparsity into variational regularization for motion estimation. The proposed regularization uses a robust l1 norm, which promotes sparsity and handles motion discontinuities. By using this regularization, we promote the sparsity of the optical flow gradient. This sparsity helps recover a signal even with just a few measurements. We explore recovering optical flow from a limited set of linear measurements using this regularizer. Our findings show that leveraging the sparsity of the derivatives of optical flow reduces computational complexity and memory needs., Comment: 12 pages, 9 figures, and 3 tables

Power splitting based simultaneous wireless information and power transfer (PS-SWIPT) appears to be a promising solution to support future self-sustainable Internet of Things (SS-IoT) networks. However, the performance of these networks is constrained by radio frequency signal strength and channel impairments. To address this challenge, intelligent reflecting surfaces (IRSs) are introduced in PS-SWIPT based SS-IoT networks to improve network efficiency by controlling signal reflections. In this article, an IRS-enabled phase cooperative framework is proposed to improve energy efficiency (EE) of the IoT network $({\mathtt {I}}^{net})$ using phase shifts of the user network $({\mathtt {U}^{net})}$, without constraining hardware resources at ${\mathtt {U}^{net}}$. We exploit transmit beamforming (BF) at access points (APs) and phase shifts optimization at the IRS end with phase effective cooperation between APs to enhance ${\mathtt {I}}^{net}$ EE performance. The maximization problem turns out to be NP-hard, so first, an alternating optimization (AO) is solved for the ${\mathtt {U}^{net}}$ using low computational complexity heuristic BF approaches, namely, transmit minimum-mean-square-error and zero-forcing BF, and phase optimization is performed using semidefinite relaxation (SDR) approach. To combat the computational complexity of AO, we also propose an alternative solution by exploiting heuristic BF schemes and an iterative algorithm, i.e., the element-wise block-coordinate descent method for phase shifts optimization. Next, EE maximization is solved for the ${\mathtt {I}^{net}}$ by optimizing the PS ratio and active BF vectors by exploiting optimal phase shifts of the ${\mathtt {U}}^{net}$. Simulation results confirm that employing IRS phase cooperation in PS-SWIPT based SS-IoT networks can significantly improve EE performance of ${\mathtt {I}^{net}}$ without constraining resources.

In this article, we considered the strong field approximation of nonlinear electrodynamics black hole and constructed its rotating counterpart by applying the modified Newman-Janis algorithm. The corresponding metric function in the strong field limit of the static black hole is identified in order to study the radius of photon sphere. However, the metric function for the rotating counterpart in the strong field limit is considered in order to study the horizon radius w.r.t spin parameter. We considered the Hamilton-Jacobi method to derive the geodesic equations for photon and constructed an orthonormal tetrad for deriving the equations for celestial coordinates in the observer's sky. Shadows, distortions and energy emission rates are investigated and the results are compared for different values of nonlinear electrodynamics parameter, charge and spin. It is found that the presence of the nonlinear electrodynamics parameter affects the shape and size of the shadows and thus the distortion in the case of rotation. It is also found that the nonlinearity of electrodynamics diminishes the flatness in the shadow due to the effect of spin and other parameters., Comment: 18 pages, 7 figures, Accepted for Publication in European Physical Journal C

The present work discusses about the existence of compact star model in the context of $f(R,T)$ gravity with $R$ as the Ricci scalar and $T$ as the trace of energy-momentum tensor $T_{\mu \nu}$. The model has been developed by considering the spherically symmetric spacetime consisting of isotropic fluid with $f(R,T)=R+2 \beta T$ with $\beta$ be the coupling parameter. The corresponding field equations are solved by choosing well known Finch-Skea {\em ansatz} [Finch, M.R., Skea, J.E.F.:{\it Class. Quantum Gravity} {\bf 6}, 467 (1989)]. For spacetime continuity we elaborate the boundary conditions by considering the exterior region as Schwarzschild metric. The unknown constants appearing in the solution are evaluated for the compact star PSR~J 1614-2230 for different values of coupling constant. The physical properties of the model, e.g., matter density, pressure, stability etc. have been discussed both analytically and graphically. This analysis showed that the geometry and matter are compatible with each other as well as the model is in stable equilibrium in the context of $f(R,\,T)$ modified gravity., Comment: Accepted in International Journal of Geometric Methods in Modern Physics on 25.05.2021