  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.
