The designing of 2-D digital differentiator is multimodal and high dimensional problem which requires large number of differentiator coefficients to be optimized, hence conventional design techniques will not lead to optimal 2-D differentiator design. Metaheuristic approaches is a good approach to handle multimodal and high dimensional problem under consideration. In this paper, a novel method for the design of FIR two-dimensional (2-D) digital differentiator with quadrantally odd symmetric properties is proposed. The coefficients of 2-D digital differentiator are computed and optimized using vortex search optimization (VSO) algorithm with the support of L₁ error objective function. The unique combination of VSO and L₁ error fitness function aids in achieving flatter magnitude response in designing of 2-D differentiator. Further, some comparative analysis with the well-known established techniques like cuckoo search algorithm (CSA), particle swarm optimization (PSO) and real coded genetic algorithm (RCGA) methodology is reported over full frequency bands, in order to demonstrate the advantage of the proposed novel 2-D digital differentiator design approach. To measure the performance of proposed system, some parameters are selected for illustration such as absolute magnitude error, mean absolute error, standard deviation and execution time. The excellence of the proposed approach is observed in approximating the ideal response of 2-D differentiator in contrast to other algorithms and to provide global optimal solution.

二维数字微分器的设计是多峰的高维问题，需要大量的微分器系数进行优化，因此传统的设计技术不会导致最优的二维微分器设计。元启发式方法是处理正在考虑的多峰和高维问题的好方法。本文提出了一种具有象限对称特性的二维（2-D）FIR数字微分器设计新方法。借助L ₁误差目标函数，使用涡旋搜索优化（VSO）算法计算和优化了二维数字微分器的系数。VSO和L ₁的独特组合误差适应度函数有助于在设计二维微分器时获得更平坦的幅度响应。此外，还报告了在整个频段上使用杜鹃搜索算法（CSA），粒子群优化（PSO）和实编码遗传算法（RCGA）方法等众所周知的成熟技术进行的比较分析，以证明该算法的优势。提出了新颖的二维数字微分器设计方法。为了测量所提出系统的性能，选择了一些参数进行说明，例如绝对幅度误差，平均绝对误差，标准偏差和执行时间。与其他算法相比，在逼近二维微分器的理想响应时观察到了所提出方法的卓越之处，并提供了全局最优解。