We present a new additive image factorization technique that treats images to be composed of multiple latent specular components which can be simply estimated recursively by modulating the sparsity during decomposition. Our model-driven {\em RSFNet} estimates these factors by unrolling the optimization into network layers requiring only a few scalars to be learned. The resultant factors are interpretable by design and can be fused for different image enhancement tasks via a network or combined directly by the user in a controllable fashion. Based on RSFNet, we detail a zero-reference Low Light Enhancement (LLE) application trained without paired or unpaired supervision. Our system improves the state-of-the-art performance on standard benchmarks and achieves better generalization on multiple other datasets. We also integrate our factors with other task specific fusion networks for applications like deraining, deblurring and dehazing with negligible overhead thereby highlighting the multi-domain and multi-task generalizability of our proposed RSFNet. The code and data is released for reproducibility on the project homepage.
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