Fig. 1. The schematic of DeepSTD and its compression performance on the CT and MRI data.

a DeepSTD decouples the medical data compression into two stages: shape encoding and texture encoding. In the former stage, we solve an optimization problem to obtain the optimal pair of forward and backward deformation fields, both parameterized as implicit neural representations (INRs). The forward deformation field registers the given data to the template while the backward deformation field is stored as shape information. In the latter stage, the registered data is passed through a pre-trained Transformer-CNN mixed encoder to extract texture information. Finally, the shape and texture information are concatenated together as the compressed data. b Visualization of an exemplar decompressed CT data by DeepSTD, for a sample from the CTSpine1K dataset¹⁸. The leftmost is a 3D rendering of the decompressed CT, with APSILR indicating the orientations: Anterior (A), Posterior (P), Superior (S), Inferior (I), Left (L), and Right (R). The middle column shows three representative slices highlighted by blue, green, and orange frames, alongside their respective residues with respect to the original data on the rightmost column. c Visualization of a decompressed MRI data volume from the Amos dataset⁵⁰, with the same layout as in (b). Panels b and c show the selected templates for CTSpine1K and Amos datasets, respectively. d Comparison of DeepSTD's compression quality and speed against the state-of-the-art (SOTA) algorithms, performed on the CTSpine1K dataset (CT modality) at 256 × compression and evaluated in terms of Mean Absolute Error (MAE) and Structural Similarity Index (SSIM). e DeepSTD's performance in comparison to baseline compressors on the Amos dataset (MRI modality) at 128 × compression, using the same legend as in (d).