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There has been an increasing demand for high-resolution image sensing technologies in recent years due to their diverse and advanced optical applications. With recent advances in nanofabrication technologies, this can be achieved through the realization of high-density pixels. However, the development of high-density and miniaturized pixels introduces challenges to the conventional color filters, which generally transmit and absorb different spectral components of light. A significant portion of the incident light is inherently lost using conventional color filters. Moreover, as the pixel size is shrunk, optical losses appear to be substantial. To address these fundamental limitations, a novel nanophotonic optical router is proposed in this work. Our router utilizes a single-layer, all-dielectric metasurface as a spectral router. The metasurface is designed through an inverse design approach that exploits adjoint sensitivity analysis. A novel figure of merit is developed and incorporated in the inverse design process, enabling the metasurface design to effectively sort and route the incoming light into four targeted channels, each corresponding to a distinct spectral component-red, green, blue, and near-infrared. We demonstrate that the proposed quad-spectral metasurface router, having a compact footprint of 2 μm×2 μm, achieves an average optical efficiency of approximately 39% across the broad spectral range, i.e., 400-850 nm, with each spectral channel exceeding an efficiency of 25%. This surpasses the maximum efficiency attainable by the conventional four-channel color filters. Our proposed quad-spectral metasurface router offers a wide range of applications in low-light imaging, image fusion, computational photography, and computer vision. In addition, this work highlights the applicability of an adjoint-based inverse design approach to accelerate the development of compact, efficient, and high-performance nanophotonic devices for the next generation of imaging and sensing systems.