Efficient Methods for Modeling Shift-Varying Operators

Many imaging systems require accurate characterization of their forward operators for reliable reconstruction. While shift-invariant systems admit efficient convolutional representations, many practical imaging systems are shift-varying and cannot be captured by classical convolution models. We propose the Shift-Varying Neural Operator, an efficient and expressive architecture for learning spatially varying linear operators directly from measurements. Our method builds on existing factorizations of spatially varying convolutions and expresses them in a learnable architecture. Each layer implements a spatially adaptive transformation constructed from a low-rank factorization of modulated convolutional bases. Our experiments show that our proposed method accurately recovers spatially varying point spread functions (PSFs) and learns interpretable operators. Furthermore, we show that the learned forward operator can be integrated into existing iterative inverse problem solvers.