Conditional Residual Decomposition for Distributed Image Compression

In distributed image compression (DIC), the compressed target representation and decoder-only side information (SI) jointly determine the reconstruction. However, existing DIC methods do not explicitly characterize the residual that remains after the compressed target representation and SI have both been used. As a result, they do not distinguish the content that can be inferred from SI from the remaining residual that cannot be determined by the available conditions, motivating generative modeling. To achieve this separation, we apply a conditional-expectation projection to the residual left by the compressed target representation, isolating the component predictable from SI from an orthogonal remainder after joint decoding. This orthogonal decomposition yields a variance partition in which the explained fraction defines SI reliability, while the remaining variance determines the minimum MSE of deterministic reconstruction. Building on this decomposition, we propose a DIC method with Conditional Residual Decomposition (CRDIC), which estimates how much the utilized SI reduces the residual left by the compressed target representation and converts this reduction into a spatial estimate of the residual remaining after joint decoding. The deterministic branch uses the SI-predictable residual component to refine the conditional reconstruction, while a stochastic branch models the remaining residual with an amplitude determined by its estimated scale. An antithetic odd projection further suppresses noise-independent corrections in the stochastic branch. Experiments on KITTI Stereo, Cityscapes, and InStereo2K demonstrate superior reconstruction fidelity and perceptual quality across multiple bitrates.