Shared Transform Learning and Half Thresholding for Tensor Restoration

Low-rank tensor models provide a global reference for removing sparse corruption, but a compact representation can omit genuine signal retained in the observations. We propose ST-HalfNet, an unfolded network with a learned shared tensor transform and Half thresholding for sparse corruption estimation. An orthogonal transform and nonuniform slice ranks are learned jointly under a total rank budget. Scaled factor updates estimate a reference for each input, and robust local regression predicts the signal omitted by that reference. Half thresholding then estimates corruption from the corrected residual. The restored image is obtained by subtracting this estimate from the observation, preserving signal outside the reference family. We establish optimal rank allocation for a fixed transform and derive a restoration error bound separating missed corruption, prediction error, and shrinkage. On full-resolution CAVE and ICVL images, ST-HalfNet achieves the highest mean PSNR across the tested salt-and-pepper densities and transfers to random-valued and sparse Gaussian corruption with unchanged weights, exceeding the strongest baseline by 2.94 to 13.14 dB in the transfer settings. Comparisons with the best clean approximation show that a learned reference can guide restoration beyond its own approximation accuracy.