Spectral images periodically captured by satellites are often obscured by clouds. For crop monitoring, cloud removal—called “declouding”—in satellite images is important, so that crop growth at a field level can be estimated from restored images. In this paper, we adopt a graph signal processing (GSP) approach to satellite image declouding to capture neighboring pixel correlations that persist over time. We first assume an atmospherical scattering model (ASM) for image formation, where observation $\mathbf{y}$ is a product of piecewise constant (PWC) target image x and piecewise planar (PWP) transmission map t. To decompose y back into $\mathbf{x}$ and $\mathbf{t}$, we formulate respective quadratic programming (QP) problems, without / with box constraints, using — graph Laplacian regularizer (GLR) / gradient graph Laplacian regularizer (GGLR) as prior, to compute $\mathbf{x} / \mathbf{t}$ alternately. For efficient optimization, we compute $\mathbf{x}$ in an unconstrained QP via conjugate gradient (CG) without matrix inverse, while we compute t in a constrained QP via proximal gradient descent (PGD). We unroll iterations of our alternating algorithm into neural layers for end-to-end data-driven parameter optimization, resulting in an interpretable, algorithm-specific feed-forward network. Experimental results show that our unrolled network outperforms model-based and pure deeplearning schemes in declouded image quality, objectively and subjectively.

We build interpretable and lightweight transformer-like neural networks by unrolling iterative optimization algorithms that minimize graph smoothness priors---the quadratic graph Laplacian regularizer (GLR) and the $\ell_1$-norm graph total variation (GTV)---subject to an interpolation constraint. The crucial insight is that a normalized signal-dependent graph learning module amounts to a variant of the basic self-attention mechanism in conventional transformers. Unlike "black-box" transformers that require learning of large key, query and value matrices to compute scaled dot products as affinities and subsequent output embeddings, resulting in huge parameter sets, our unrolled networks employ shallow CNNs to learn low-dimensional features per node to establish pairwise Mahalanobis distances and construct sparse similarity graphs. At each layer, given a learned graph, the target interpolated signal is simply a low-pass filtered output derived from the minimization of an assumed graph smoothness prior, leading to a dramatic reduction in parameter count. Experiments for two image interpolation applications verify the restoration performance, parameter efficiency and robustness to covariate shift of our graph-based unrolled networks compared to conventional transformers.