Denoising of astrophysical image mixtures from nonstationary noise by vertex-frequency graph Wiener filtering

Astrophysical image mixtures, consisting of various components including cosmic microwave background radiation, galactic dust and synchrotron, are infected by nonstationary instrumental noise with space varying power. To denoise such image mixtures, we first propose a spectral graph based vertex-frequency Wiener filter for denoising of graph signals defined on weighted, undirected and connected graphs from nonstationary noise. Assuming that an original, noiseless image mixture can be viewed as a deterministic graph signal over a regular two-dimensional graph, we then propose a graph lowpass filter based denoising algorithm that estimates the proposed graph Wiener filter from the input, noisy mixture to apply for its denoising. We compare our algorithm with five prominent image denoising methods for image mixtures simulated to be received through 100 GHz and 70 GHz microwave channels, for various mixing coefficients. In terms of obtained peak signal-to-noise ratio figures, our algorithm is slightly surpassed by the nonlocal means method improved by the Sinkhorn algorithm (NLM+S) in all mixing scenarios, but is generally competitive with other compared denoising methods, and has computational cost advantage against the NLM+S method. Comparisons reveal that our proposed algorithm could be the choice for denoising 70 GHz mixtures with low or medium galactic contamination from nonstationary instrumental noise.