Quantum advantages for image filtering on images with efficient encoding and lower-bounded signal-to-noise ratio

Quantum image processing has long been a fascinating field, but establishing the existence of quantum speedup for all images remains challenging. In this study, we aim to identify a subset of images for which a quantum algorithm can be developed with a guaranteed advantage. Specifically, we present a quantum image filtering algorithm that exhibits an exponential speedup for efficiently encoded images with a lower-bounded signal-to-noise ratio. Our approach relies on a fixed-point Grover’s search to emulate the effect of Hadamard multiplication with the filtering function. To demonstrate its effectiveness, we apply our method to three typical filtering problems. Additionally, we emphasize the significance of the efficient-encoding assumption by illustrating that the quantum speedup may diminish for images lacking efficient encoding. Our work underscores the importance of exploring image types and features to realize potential quantum advantages in image processing.