An innovative method for image demosaicking is introduced, leveraging perceptual-based tone mapping, secondorder polynomial interpolation filters, and Quantum-Inspired Optimization to achieve superior image reconstruction quality. The proposed approach integrates an Autoregressive Wavelet Water Optimization (WWO) algorithm to determine coefficients for second-order polynomial filters within the LPA-ICI framework. Simultaneously, a Deep Convolutional Neural Network (Deep CNN) is employed to generate residual images, capturing intricate features. The outputs of the interpolation-based method and the Deep CNN are fused using an entropy-based metric, resulting in enhanced visual quality and reduced artifacts in the demosaicked images. Perceptual-based tone mapping is applied to address brightness discrepancies, ensuring luminance accuracy and improved image realism. Additionally, Quantum-Inspired Optimization enhances the efficiency and robustness of the filtering process. Experimental results demonstrate significant improvements in reconstruction accuracy, making the proposed method a promising alternative for applications requiring precise and visually appealing demosaicking. Future work will explore the extension of this method to multispectral images and address the challenges of real-time processing.