Quantum implementation of the classical guided image filtering algorithm

Image filtering involves the application of window operations that perform valuable functions, such as noise removal, image enhancement, high dynamic range (HDR) compression, and so on. Guided image filtering is a new type of explicit image filter with multiple advantages. It can effectively remove noise while preserving edge details, and can be used in a variety of scenarios. Here, we report a quantum implementation of guided image filtering algorithm, based on the novel enhanced quantum representation (NEQR) model, and the corresponding quantum circuit has been designed. We find that the speed and quality of filtering are improved significantly due to the quantization, and the time complexity is reduced exponentially from $O\left(2^{2q}\right)$ to $O\left(q^2\right)$ .