A quantum synthetic aperture radar image denoising algorithm based on grayscale morphology.

The quantum denoising technology efficiently removes noise from images; however, the existing algorithms are only effective for additive noise and cannot remove multiplicative noise, such as speckle noise in synthetic aperture radar (SAR) images. In this paper, based on the grayscale morphology method, a quantum SAR image denoising algorithm is proposed, which performs morphological operations on all pixels simultaneously to remove the noise in the SAR image. In addition, we design a feasible quantum adder to perform cyclic shift operations. Then, quantum circuits for dilation and erosion are designed, and the complete quantum circuit is then constructed. For a 2n×2n quantum SAR image with q grayscale levels, the complexity of our algorithm is O (n+q). Compared with classical algorithms, it achieves exponential improvement and also has polynomial-level improvements than existing quantum algorithms. Finally, the feasibility of our algorithm is validated on IBM Q.