FROM LOW-RANK TO SKETCH: CHEBYSHEV-GUIDED UNFOLDING FOR EFFICIENT PANSHARPENING

Pansharpening fuses a high-resolution panchromatic image with a low-resolution multispectral image. Existing methods repeatedly transform high-dimensional features, incurring cost that scales with feature dimensions and resolution. Motivated by the strong inter-band correlation and spatial-spectral redundancy of multispectral images, we design efficient sketch operators that confine the principal transformations to compact channel and spatial subspaces. To avoid the instability of repeatedly performing singular value decomposition (SVD) inside a deep network, we introduce a Chebyshev-Guided Approximation Mechanism that constructs adaptive, approximately row-orthogonal projections directly from Gram statistics. We further introduce a nullspace compensation mechanism to preserve information outside the selected subspaces. In the resulting multigrid-inspired unfolding architecture, termed OSSNet, CSS and CCS respectively provide dataadaptive spatial restriction with adjoint prolongation and compact channel routing at the coarsest level. Level-wise residual-correction blocks refine features before restriction, while coarse representations are prolonged and fused with complementary residuals during decoding. Experiments show that OSSNet achieves competitive reconstruction performance with low parameter count, measured latency, and computational cost.