Chengshuai Yang

Chengshuai Yang

Computational imaging forward models, from coded aperture spectral cameras to MRI scanners, are traditionally implemented as monolithic, modality-specific codes. We prove that every forward model in a broad, precisely defined operator class Cimg (encompassing clinical, scientific, and industrial imaging modalities, both linear and nonlinear) admits an epsilon-approximate representation as a typed directed acyclic graph (DAG) whose nodes are drawn from a library of exactly 11 canonical primitives: Propagate, Modulate, Project, Encode, Convolve, Accumulate, Detect, Sample, Disperse, Scatter, and Transform. We call this the Finite Primitive Basis Theorem. The proof is constructive: we provide an algorithm that, given any H in Cimg, produces a DAG G with relative operator error at most epsilon and graph complexity within prescribed bounds. We further prove that the library is minimal: removing any single primitive causes at least one modality to lose its epsilon-approximate representation. A systematic analysis of nonlinearities in imaging physics shows they fall into two structural categories: pointwise scalar functions (handled by Transform) and self-consistent iterations (unrolled into existing linear primitives). Empirical validation on 31 linear modalities confirms eimg below 0.01 with at most 5 nodes and depth 5, and we provide constructive DAG decompositions for 9 additional nonlinear modalities. These results establish mathematical foundations for the Physics World Model (PWM) framework.

Chengshuai Yang, Xin Yuan

Computational imaging systems -- from coded-aperture cameras to cryo-electron microscopes -- span five carrier families yet share a hidden structural simplicity. We prove that every imaging forward model decomposes into a directed acyclic graph over exactly 11 physically typed primitives (Finite Primitive Basis Theorem) -- a sufficient and minimal basis that provides a compositional language for designing any imaging modality. We further prove that every reconstruction failure has exactly three independent root causes: information deficiency, carrier noise, and operator mismatch (Triad Decomposition). The three gates map to the system lifecycle: Gates 1 and 2 guide design (sampling geometry, carrier selection); Gate 3 governs deployment-stage calibration and drift correction. Validation across 12 modalities and all five carrier families confirms both results, with +0.8 to +13.9 dB recovery on deployed instruments. Together, the 11 primitives and 3 gates establish the first universal grammar for designing, diagnosing, and correcting computational imaging systems.

Chengshuai Yang, Xin Yuan

State-of-the-art EfficientSCI loses 20.58 dB when its assumed forward operator deviates from physical reality in just eight parameters, yet no existing benchmark quantifies operator mismatch, the default condition in deployed compressive imaging systems. We introduce InverseNet, the first cross-modality benchmark for operator mismatch, spanning CASSI, CACTI, and single-pixel cameras. Evaluating 12 methods under a four-scenario protocol (ideal, mismatched, oracle-corrected, blind calibration) across 27 simulated scenes and 9 real hardware captures, we find: (1) deep learning methods lose 10-21 dB under mismatch, eliminating their advantage over classical baselines; (2) performance and robustness are inversely correlated across modalities (Spearman r_s = -0.71, p < 0.01); (3) mask-oblivious architectures recover 0% of mismatch losses regardless of calibration quality, while operator-conditioned methods recover 41-90%; (4) blind grid-search calibration recovers 85-100% of the oracle bound without ground truth. Real hardware experiments confirm that simulation trends transfer to physical data. Code will be released upon acceptance.