Hybrid classical-quantum image processing via polar Walsh basis functions

Abstract: We propose a novel hybrid classical-quantum approach for image processing based on polar Walsh basis functions. Using this approach, we present an algorithm for the removal of the circular banding noise (including Airy pattern noise) and the azimuthal banding noise. This approach is based on a formulation of Walsh basis functions in polar coordinates for image representations. This approach also builds upon an earlier work on a hybrid classical-quantum algorithm for Walsh-Hadamard transforms. We provide two kinds of polar representations using uniform area measure and uniform radial measure. Effective smoothening and interpolating techniques are devised relevant to the transformations between Cartesian and polar coordinates, mitigating the challenges posed by the non-injectivity of the transformation in the context of digital images. The hybrid classical-quantum approach presented here involves an algorithm for Walsh-Hadamard transforms, which has a lower computational complexity of $\mathcal{O}(N)$ compared to the well-known classical Fast Walsh-Hadamard Transform, which has a computational complexity of $\mathcal{O}(N \log_2 N)$. We demonstrated the applicability of our approach through computational examples involving the removal of the circular banding noise (including Airy pattern noise) and the azimuthal banding noise.