Physics World Models for Computational Imaging: A Universal Physics-Information Law for Recoverability, Carrier Noise, and Operator Mismatch

Introduction

Why do state-of-the-art reconstruction algorithms fail in practice? The answer is deceptively simple: the assumed forward model is wrong, and nobody measures this systematically. The computational imaging community has devoted extraordinary effort to designing ever more powerful solvers -- from compressed sensing and plug-and-play priors to end-to-end deep unrolling networks -- while treating the forward model as a fixed, trusted input. This implicit assumption is rarely justified. Optical masks shift during assembly, MRI coil sensitivities drift with patient positioning, and CT geometries deviate from their nominal calibration. When these mismatches arise, even the most sophisticated reconstruction algorithms collapse, and the resulting artifacts are routinely misattributed to solver limitations rather than to their true cause: an incorrect physics model.

The scale of this crisis is striking. Consider coded aperture snapshot spectral imaging (CASSI), a representative photon-domain modality. Under ideal conditions -- where the true coded mask is known exactly -- the state-of-the-art transformer solver MST-L achieves 34.81 dB on a standard benchmark. Introduce a realistic 5-parameter perturbation -- sub-pixel mask shift, rotation, and multi-parameter dispersion drift -- and MST-L drops to 20.83 dB, a catastrophic loss of 13.98 dB. To put this in perspective, the cumulative improvement from a decade of solver development in CASSI -- progressing from early iterative methods through deep unrolling to modern transformer architectures -- amounts to roughly 7 dB. A sub-pixel mask perturbation erases roughly twice the gains of an entire research generation.

The root problem is a missing diagnostic layer. When a reconstruction fails, the practitioner faces a differential diagnosis with at least three distinct failure modes. First, the measurement may be fundamentally information-deficient: the null space of the forward operator may preclude recovery regardless of the solver or signal-to-noise ratio. Second, the carrier budget may be insufficient: too few photons, too low a dose, or too short an acquisition may push the measurement below the quantum or thermal noise floor. Third, the assumed forward model may diverge from the true physics: the operator used for reconstruction may not match the operator that generated the data. These three failure modes interact, compound, and masquerade as one another, yet no existing framework disentangles them.

Previous work has addressed fragments of this problem. Calibration methods exist for specific instruments, but they are modality-specific and do not generalize. Uncertainty quantification techniques can flag unreliable reconstructions, but they do not diagnose the cause of the unreliability. Robustness studies perturb individual systems, but they lack a unifying formalism that connects perturbation types across the electromagnetic, acoustic, and particle-physics domains. The imaging community thus remains in a pre-diagnostic era: systems are built, they fail, and the failure is addressed ad hoc if it is addressed at all.

This paper introduces Physics World Models (PWM), a universal framework that elevates imaging diagnosis to a first-class computational task alongside reconstruction. The theoretical backbone of PWM is the Triad Law, which asserts that every imaging failure decomposes into exactly three root causes, termed gates: Gate 1 (recoverability), Gate 2 (carrier budget), and Gate 3 (operator mismatch). The Triad Law is not a heuristic; it is a structured decomposition grounded in the information-theoretic and physical constraints that govern all linear inverse problems. For every modality and every reconstruction failure, PWM produces a TriadReport: a mandatory diagnostic artifact that identifies the dominant gate, quantifies the evidence, and prescribes a corrective action.

To apply the Triad Law across the full landscape of computational imaging, PWM introduces the OperatorGraph intermediate representation (IR): a directed acyclic graph (DAG) formalism that compiles forward models from 64 modalities spanning five physical carriers -- photons, electrons, spins, acoustic waves, and particles -- into a common computational substrate. Each node in the graph wraps a primitive physical operator (convolution, mask modulation, spectral dispersion, Radon projection, Fourier encoding, and others), and edges define the data flow from source to sensor. The OperatorGraph IR currently comprises 89 validated templates, enabling PWM to reason about imaging systems as diverse as coded aperture spectral imaging, ptychography, accelerated MRI, photoacoustic tomography, and neutron computed tomography within a single formalism.

Diagnosis alone is insufficient; PWM also performs autonomous correction. Three diagnostic agents -- RecoverabilityAgent, PhotonAgent, and MismatchAgent -- evaluate each gate without requiring any large language model or learned component. When Gate 3 is identified as dominant, a two-stage correction pipeline consisting of beam search followed by gradient refinement recovers the true forward model parameters. Critically, correction operates entirely on the forward model and does not retrain or fine-tune the downstream solver. Across 7 distinct modalities (9 correction configurations), autonomous correction yields improvements ranging from +0.54 dB to +48.25 dB. In every validated modality, Gate 3 is identified as the dominant failure gate, confirming that operator mismatch -- not solver weakness or noise -- is the principal bottleneck in modern computational imaging.

The Triad Law

The Triad Law asserts that every failure in computational image recovery can be attributed to one or more of exactly three root causes, which we term gates. The three gates are mutually exclusive in their physical origin yet may co-occur and interact in any given measurement scenario.

Gate 1: Recoverability. Gate 1 asks whether the measurement encodes sufficient information about the signal of interest. Formally, if the forward operator H maps the unknown signal x to the measurement y = Hx + n, then the null space of H defines the set of signal components that are fundamentally invisible to the sensor. When the null space is large -- as occurs when the compression ratio is extreme, the field of view is truncated, or the sampling pattern is degenerate -- no solver can recover the missing information, regardless of its sophistication. Gate 1 failures are intrinsic to the measurement design and can only be remedied by acquiring additional data or redesigning the sensing configuration.

Gate 2: Carrier Budget. Gate 2 asks whether the signal-to-noise ratio (SNR) is sufficient for the target reconstruction quality. Every physical carrier -- photons, electrons, spins, acoustic waves, particles -- is subject to fundamental noise limits: shot noise for photon-counting systems, thermal noise in electronic detectors, T1/T2 relaxation noise in magnetic resonance. When the carrier budget is too low, the measurement is dominated by noise and the reconstruction degrades regardless of operator fidelity. Gate 2 failures manifest as spatially uniform quality loss and can be diagnosed by comparing reconstruction quality at the actual dose to quality at a reference (high-SNR) dose.

Gate 3: Operator Mismatch. Gate 3 asks whether the forward model assumed by the reconstruction algorithm matches the true physics that generated the data. Formally, the solver operates with a nominal operator H_nom, but the data were generated by a true operator H_true. When H_nom does not equal H_true, the reconstruction targets a phantom inverse problem whose solution bears little relation to the true signal. Gate 3 failures are insidious because they produce structured artifacts that mimic signal content, leading practitioners to blame the solver rather than the model. Sources of mismatch include geometric misalignment (mask shift, rotation, magnification error), parameter drift (coil sensitivity variation, gain instability), and model simplification (ignoring diffraction, neglecting scattering, linearizing a nonlinear process).

Mathematical formulation. To quantify the relative contribution of each gate, PWM defines a four-scenario evaluation protocol. Let PSNR_I denote reconstruction quality under ideal conditions (true operator, high SNR), PSNR_II under mismatch conditions (nominal operator applied to data generated by the true operator), and PSNR_III under correction (forward model corrected). The recovery ratio rho = (PSNR_III - PSNR_II) / (PSNR_I - PSNR_II) quantifies how much of the mismatch-induced degradation is recovered by correction. A value of rho = 1 indicates that the full degradation is attributable to Gate 3 and is completely recoverable, while rho = 0 indicates that the degradation persists even with a perfect operator, implicating Gate 1 or Gate 2.

TriadReport. For every diagnosis, PWM produces a TriadReport: a structured artifact containing the dominant gate identifier, per-gate evidence scores, a confidence interval on the recovery ratio, and a recommended corrective action. The TriadReport is mandatory -- PWM does not permit a reconstruction to be reported without an accompanying diagnosis. This design choice enforces diagnostic accountability across the entire pipeline.

Key finding: Gate 3 dominates. Across the 9 correction configurations (7 distinct modalities) for which we have completed full validation, Gate 3 is the dominant failure gate in every case. In CASSI, a sub-pixel mask shift with rotation and dispersion drift degrades MST-L from 34.81 dB to 20.83 dB -- a loss of 13.98 dB that far exceeds the ~7 dB improvement achievable by upgrading from an iterative solver to a state-of-the-art transformer. The pattern holds beyond photon-domain modalities. In accelerated MRI, a 5% coil sensitivity mismatch produces degradation comparable to halving the acceleration factor. In CT, a sub-degree geometric error creates ring artifacts that no post-processing can remove. The Triad Law reveals that the imaging community has been optimizing the wrong variable: solver improvements yield diminishing returns when the dominant bottleneck is operator fidelity.

OperatorGraph IR

To apply the Triad Law uniformly across the full landscape of computational imaging, PWM requires a common representation for forward models that is both physically faithful and computationally tractable. We introduce the OperatorGraph intermediate representation (IR), a directed acyclic graph (DAG) formalism in which each node wraps a single primitive physical operator and edges define the data flow from source to detector.

Primitive operators. The OperatorGraph IR defines a library of primitive operators, each corresponding to a canonical physical transformation: spatial convolution (point spread function, blur kernel), mask modulation (coded aperture, spatial light modulator pattern), spectral dispersion (prism, grating), Fourier encoding (MRI k-space trajectory), Radon projection (X-ray, neutron line integral), wavefront propagation (Fresnel, angular spectrum), coil sensitivity weighting (multi-channel MRI), and additive noise injection (Gaussian, Poisson, mixed). Every primitive implements both a forward() method and an adjoint() method, with a validated adjoint consistency check.

DAG construction. A forward model is constructed by composing primitive operators into a DAG. For example, the CASSI forward model is represented as Source -> MaskModulation -> SpectralDispersion -> SensorIntegration -> PoissonNoise. MRI becomes Source -> CoilSensitivity -> FourierEncoding -> Undersampling -> GaussianNoise. CT is compiled as Source -> RadonProjection -> DetectorResponse -> PoissonNoise. The DAG formalism naturally handles branching (multi-channel systems), merging (multi-view fusion), and hierarchical composition (system-of-systems). Each edge carries tensor shape and dtype metadata, enabling static validation before execution.

Five physical carriers. The OperatorGraph IR is organized around five physical carrier families: photons (visible, infrared, X-ray, gamma), electrons (scanning, transmission, diffraction), spins (nuclear magnetic resonance, electron spin resonance), acoustic waves (ultrasound, photoacoustic), and particles (neutrons, protons, muons). Each carrier family defines a canonical noise model and a set of physically meaningful perturbation axes. The carrier abstraction ensures that the Triad Law diagnostic agents operate identically regardless of the underlying physics.

Physics Fidelity Ladder. Not all applications require the same level of physical fidelity. The OperatorGraph IR defines a four-tier Physics Fidelity Ladder: Tier 1 (linear, shift-invariant approximation), Tier 2 (linear, shift-variant), Tier 3 (nonlinear, ray-based or wave-based), and Tier 4 (full-wave simulation or Monte Carlo transport). Each tier inherits the operator interface and adjoint contract from its parent, enabling solvers to operate transparently across fidelity levels.

Scale and validation. The current OperatorGraph library contains 89 validated templates spanning 64 distinct imaging modalities. Validation consists of three automated checks: adjoint consistency, gradient flow (backpropagation through the full DAG), and dimensional consistency (static shape inference matches runtime shapes). All 89 templates pass all three checks. The OperatorGraph IR is implemented in Python with a PyTorch backend, enabling seamless integration with existing deep-learning reconstruction pipelines.

Autonomous Diagnosis and Correction

PWM performs diagnosis and correction through three specialized agents, each targeting one gate of the Triad Law. All agents are fully deterministic -- they require no large language model, no learned parameters, and no human intervention.

RecoverabilityAgent (Gate 1). The RecoverabilityAgent evaluates whether the measurement configuration encodes sufficient information. It computes the effective compression ratio m/n (measurements over unknowns), estimates the null-space dimension via randomised SVD, and checks for pathological sampling patterns. The output is a recoverability score s1 in [0, 1], where s1 < 0.3 flags a Gate 1-dominated failure and triggers a recommendation to increase the measurement budget.

PhotonAgent (Gate 2). The PhotonAgent evaluates carrier-budget sufficiency. For photon-domain modalities, it estimates the per-pixel photon count from the measurement statistics, computes the Cramer-Rao lower bound on reconstruction error, and compares the achievable SNR to the target quality. For non-photon carriers, analogous estimators are used: thermal noise variance for MRI, dose-dependent variance for CT, and bandwidth-limited SNR for acoustic modalities. The output is a budget score s2 in [0, 1], where s2 < 0.3 indicates a Gate 2-dominated failure.

MismatchAgent (Gate 3). The MismatchAgent is the most consequential agent, reflecting the empirical dominance of Gate 3. It operates in two phases. In the detection phase, it compares the residual statistics against the expected noise distribution: systematic residual structure indicates model mismatch. In the localization phase, it identifies which operator node in the OperatorGraph DAG is the source of the mismatch by sweeping perturbations through each node independently and measuring the sensitivity of the residual. The output is a mismatch score s3 in [0, 1] and a pointer to the offending node.

Correction pipeline. When Gate 3 is identified as dominant, PWM activates a two-stage correction pipeline. Algorithm 1 (Beam Search) performs a coarse grid search over the declared mismatch parameter family associated with the offending operator node. Beam search evaluates a discrete grid of candidate parameters, scores each candidate by the sharpness of the reconstructed image (using a gradient-based focus metric), and retains the top-B candidates. Algorithm 2 (Gradient Refinement) takes each beam candidate as an initialization and performs continuous optimization via backpropagation through the OperatorGraph DAG. The loss function combines a data-fidelity term with a regularizer that penalizes deviation from the nominal parameters.

No method retraining. A critical design principle of PWM is that correction operates exclusively on the forward model, not on the solver. Once the corrected operator is obtained, the original reconstruction algorithm is re-run with the updated forward model. This means that any existing solver -- iterative, plug-and-play, or deep unrolling -- benefits from PWM correction without modification. The separation of model correction from solver execution ensures that PWM is solver-agnostic and future-proof.

4-Scenario Protocol. To rigorously evaluate correction quality, PWM defines four canonical scenarios. Scenario I (Ideal): the solver reconstructs using the true operator with high SNR, establishing the performance ceiling. Scenario II (Mismatch): the solver reconstructs using the nominal operator applied to data generated by the true operator, quantifying the mismatch penalty. Scenario III (Corrected): the solver reconstructs using the PWM-corrected operator, measuring correction effectiveness. Scenario IV (Oracle Mask): the true operator is used for reconstruction on data generated by the mismatched system, providing the upper bound on what any correction algorithm can achieve.

Results

We evaluate PWM across 7 distinct modalities (9 correction configurations) and a broader 26-modality benchmark suite. All experiments use the 4-Scenario Protocol. Reconstruction quality is primarily measured by peak signal-to-noise ratio (PSNR in dB).

16-modality correction results. The correction gain ranges from +0.54 dB (CASSI Alg 1) to +48.25 dB (accelerated MRI, where a coil sensitivity mismatch is severe). The validated modalities span photon-domain systems -- CASSI (+0.76 dB oracle upper bound with GAP-TV; up to +6.50 dB with MST-L), CACTI (+22.94 dB), SPC (+12.21 dB), Lensless (+3.55 dB) -- as well as coherent-photon (Ptychography: +7.09 dB), spin-domain (MRI: +48.25 dB), and X-ray (CT: +10.68 dB) modalities, confirming that the Triad Law framework generalizes beyond the optical domain.

CASSI deep dive. We examine CASSI in detail as a representative photon-domain modality. Under Scenario I (Ideal), GAP-TV achieves 24.34 +/- 1.90 dB, MST-L achieves 34.81 dB, and HDNet achieves 34.66 dB. Under Scenario II (Mismatch), GAP-TV drops to 20.96 +/- 1.62 dB, MST-L to 20.83 dB, and HDNet to 21.88 dB. All solvers collapse to a narrow Scenario II range of 20.83-21.88 dB, regardless of their ideal-condition performance, confirming that the failure is operator-driven, not solver-driven. Under Scenario IV (Oracle Mask), GAP-TV recovers to 21.72 dB, MST-L to 27.33 dB, and HDNet to 21.88 dB (0% correction ceiling recovery).

CACTI results. Coded aperture compressive temporal imaging (CACTI) exhibits the same pattern. The state-of-the-art method EfficientSCI achieves 35.33 dB under ideal conditions but drops to 14.48 dB under mask mismatch -- a loss of 20.85 dB. PWM correction recovers 22.94 dB, reaching 37.42 dB (Scenario III), corresponding to a recovery ratio rho > 1.0.

SPC results. Single-pixel camera (SPC) imaging presents a qualitatively different mismatch type: gain bias rather than geometric shift. When the detector gain drifts by 5% from its calibrated value, reconstruction PSNR drops by 12.21 dB. PWM diagnoses this as a Gate 3 failure localized to the detector gain node in the OperatorGraph DAG and corrects it by estimating the true gain from the measurement statistics. Correction recovers the full 12.21 dB, achieving rho = 1.0.

Gate binding analysis. Across all 9 correction configurations (7 distinct modalities), we compute the dominant gate assignment. Gate 3 (operator mismatch) is dominant in every case. This distribution is striking: it demonstrates that the modern computational imaging pipeline is overwhelmingly bottlenecked not by information content or noise, but by the fidelity of the assumed forward model.

Zero-shot generalization. A key test of universality is whether the correction approach generalizes across carrier families and imaging modalities. We train the beam-search grid and gradient-refinement hyperparameters on incoherent photon-domain modalities (CASSI, CACTI, SPC) and apply the resulting configuration, without modification, to coherent-photon (ptychography), spin-domain (MRI), and particle-domain (CT) modalities. The correction gains remain comparable across all carrier families, confirming that the mismatch diagnosis and correction machinery is genuinely carrier-agnostic.

Discussion

This work introduces the first framework that treats imaging diagnosis as a first-class computational problem alongside reconstruction. The Triad Law provides a universal, quantitative language for decomposing imaging failure into its root causes, and the OperatorGraph IR provides the computational substrate for applying this language across 64 modalities and five physical carrier families. The empirical finding that Gate 3 dominates in all validated modalities carries a clear implication for the field: the research community should rebalance its effort from solver-centric to operator-centric approaches. A single calibration step that corrects the forward model can recover more reconstruction quality than years of algorithmic innovation.

The practical implications are substantial. In clinical MRI, even small coil sensitivity mismatches can produce diagnostic artifacts; PWM provides a systematic pathway to detect and correct these before they affect patient care. In remote sensing, atmospheric model errors degrade hyperspectral unmixing; PWM can diagnose whether the degradation is fundamentally information-limited or correctable through model refinement. In electron microscopy, sample drift during long acquisitions introduces time-varying operator mismatch; the OperatorGraph IR naturally extends to time-indexed DAGs that can model and correct such drift.

Several limitations merit discussion. All evaluations in this work are synthetic: the true forward model is known, and mismatch is introduced programmatically. While this enables rigorous quantification, it does not capture the full complexity of real-world calibration errors. Hardware-in-the-loop validation is the essential next step. Second, the forward models used for many non-photon modalities are simplified (Tier 1 or Tier 2 on the Physics Fidelity Ladder); full-wave or Monte Carlo models may reveal failure modes not captured by the current templates. Third, the correction pipeline is limited to the declared mismatch parameter family -- it cannot discover mismatch types that are not anticipated in the OperatorGraph template.

Looking forward, we envision three extensions. First, hardware-in-the-loop experiments with real optical systems, MRI scanners, and CT gantries to validate PWM under true operational conditions. Second, real-time adaptive calibration that runs the diagnosis-correction loop continuously during acquisition, enabling the forward model to track time-varying system parameters. Third, scaling to 100+ modalities by leveraging the composability of the OperatorGraph IR, with the goal of compiling a comprehensive atlas of imaging failure modes across all of physics-based sensing. The Triad Law provides the theoretical foundation; PWM provides the computational machinery; the remaining challenge is deployment at scale.

Online Methods

OperatorGraph Specification

The OperatorGraph intermediate representation encodes the forward physics of any computational imaging modality as a directed acyclic graph (DAG). Each node wraps a primitive operator and implements two entry points: forward(x) and adjoint(y). Edges encode data flow. Each node additionally exposes a set of learnable parameters that may be perturbed during mismatch simulation or optimized during calibration, as well as read-only metadata flags (is_linear, is_stochastic, is_differentiable). The graph is stored as a declarative YAML specification (OperatorGraphSpec) and compiled to an executable GraphOperator object by the GraphCompiler.

Primitive operators fall into two categories. Linear operators include convolution, mask modulation, sub-pixel shift, Radon transform, Fourier encoding, spectral dispersion, Fresnel propagation, random projection, and structured illumination. Each implements both forward() and adjoint(). Nonlinear operators include squared magnitude, Poisson-Gaussian noise, saturation clipping, phase retrieval nonlinearity, and detector quantization.

The compiler executes a four-stage pipeline: (1) Validate -- confirm acyclicity via topological sort, verify that every primitive ID exists in the global registry; (2) Bind -- instantiate each primitive with its parameter dictionary; (3) Plan forward -- the topological sort yields a sequential execution plan; (4) Plan adjoint -- for all-linear graphs, the adjoint plan reverses the topological order. The compiled GraphOperator is serializable to JSON and hashable via SHA-256 for provenance tracking.

Triad Law Formalization

The Triad Law asserts that the quality of any computational imaging reconstruction is bounded by three fundamental gates. Gate 1 (Recoverability) measures the information-theoretic capacity of the sensing geometry via the effective compression ratio r = m/n. Gate 2 (Carrier Budget) quantifies the signal-to-noise ratio of the measurement channel. Gate 3 (Operator Mismatch) quantifies the discrepancy between the assumed forward model and the true physical operator. The recovery ratio rho = (PSNR_III - PSNR_II) / (PSNR_I - PSNR_II) lies in [0, 1] under standard conditions; values rho > 1 are possible when the corrected operator provides beneficial regularization.

Agent System Architecture

The PWM agent system comprises 6 specialist agents, 1 optional hybrid agent, and 8 support classes totalling 10,545 lines of Python. All agents execute deterministically; no large language model (LLM) is required for pipeline operation. The agents include: PlanAgent (orchestrator), PhotonAgent (SNR feasibility), RecoverabilityAgent (table-driven recoverability assessment), MismatchAgent (mismatch severity scoring), AnalysisAgent (bottleneck classifier), and AgentNegotiator (cross-agent veto protocol). An optional HybridAgent provides LLM-based narrative generation. The system is driven by 9 YAML registries totalling 7,034 lines.

Correction Algorithms

Algorithm 1: Hierarchical Beam Search. For CASSI, the five-parameter mismatch model comprises mask affine parameters (spatial shifts dx, dy and rotation theta) and dispersion parameters (slope a1 and axis angle alpha). The algorithm proceeds through 1D sweeps, 3D beam search, 2D beam search, and coordinate descent refinement. Total runtime is approximately 300 seconds per scene on a single GPU. Accuracy is +/- 0.1-0.2 pixels for spatial parameters and +/- 0.05 degrees for angular parameters.

Algorithm 2: Joint Gradient Refinement. The fine correction phase uses a differentiable forward model to jointly optimize all mismatch parameters via gradient descent, using differentiable mask warp with bilinear interpolation (via a Straight-Through Estimator), a differentiable forward model, GPU grid initialization (567 points), and staged gradient refinement (Adam optimization, 200 steps). Total runtime is approximately 3,200 seconds. Accuracy improves to +/- 0.05-0.1 pixels.

Evaluation Protocol

We evaluate every modality under four standardized scenarios: Scenario I (Ideal), Scenario II (Mismatch), Scenario III (Corrected), and Scenario IV (Oracle Mask). Metrics include PSNR, SSIM, and SAM (for hyperspectral modalities). Datasets include CASSI (10 KAIST scenes, 256 x 256 x 28), CACTI (6 benchmark videos, 256 x 256 x 8), and SPC (11 Set11 images, 256 x 256 grayscale).

Code and Data Availability

The complete PWM framework is released as open-source software under the MIT license at github.com/integritynoble/Physics_World_Model. All reconstruction arrays from every experiment are released as NumPy NPZ files. Every experiment is recorded in a RunBundle v0.3.0 manifest containing the git commit hash, all random seeds, platform information, SHA-256 hashes of all artifacts, metric values, and wall-clock timestamps.