Photoacoustic-Ultrasound Dual-mode Imaging (PAUS) L1-509

Medical ImagingConcurrent functional + anatomical imaging via dual-contrast acquisition (multi-physics joint inverse)δ=5 · advancedL_DAG = 9.5📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

P A c hain : P hi = G_{o} pt i c a l \cdot S; H = m u_{a} \cdot P hi; p_{0} = G amma \cdot H; p_{P} A (r_{d}, t, λ) = in t e g r a l G_{a} co u s t i c (r_{d}, r^{'}; c) \cdot p_{0} (r^{'}, λ) d r^{'} + n_{P} A . U S c hain : y_{U} S (r_{d}, t) = in t e g r a l G_{p} u l s e_{e} c h o (r_{d}, r^{'}; c, r h o) \cdot (d e l t a - Z / Z) (r^{'}) d r^{'} + n_{U} S . J o in t in v er s i o n : r eco v er (m u_{a} (r, λ), Z (r), c (r), r h o (r)) f r o mj o in t p_{P} A, y_{U} S g i v e nm u_{s}^{'}, G amma, o pt i c a l i l l u mina t i o n S, U S t r an s mi t b e am .

Photoacoustic-Ultrasound Dual-mode Imaging (PAUS): joint multi-physics forward couples (i) qPAT chain — optical fluence Phi(r, lambda) by radiative transfer, energy absorption H = mu_a * Phi, thermoelastic source p_0 = Gamma * H, acoustic propagation p_PA(r_d, t) = integral G_acoustic(r_d, r'; c) * p_0(r') dr'; (ii) pulse-echo ultrasound — incident wave from US transmit produces backscatter from tissue impedance contrast Z(r) = rho(r) * c(r), with received signal y_US(r_d, t) = integral G_pulse_echo(r_d, r'; c, rho) * (delta-Z/Z)(r') dr' under the Born approximation; (iii) shared tissue model — both modalities depend on the same tissue speed-of-sound c(r) and density rho(r) maps, with PA additionally constrained by mu_s'(r) and qPAT-specific parameters. The forward DAG has 9 primitives with two coupling constraints (n_c = 2): (i) shared tissue speed-of-sound and density across both modalities (parameter coupling); (ii) spatially co-registered acquisition (geometric coupling — same transducer, same scan plane). Recovery is posed as the joint inverse problem that recovers (mu_a(r, lambda), Z(r), c(r), rho(r)) from joint measurement {p_PA(r_d, t, lambda), y_US(r_d, t)}. Difficulty tier delta = 5 with raw condition number kappa ~ 280 (limited by PA/US bandwidth mismatch and absorbing-region ambiguity) and effective kappa_eff ~ 40 after model-based joint reconstruction. Mismatch parameters: pa_us_synchronization_jitter, fluence_inhomogeneity, acoustic_speed_heterogeneity, acoustic_attenuation, transducer_bandwidth_difference_pa_vs_us, motion_during_acquisition. Additive Gaussian thermal noise sets the data-fidelity floor. See forward_model field for the closed-form joint imaging equation.

L-DAG

L.optical_source -> L.optical_diffusion -> L.beer_lambert -> L.thermoelastic_grueneisen -> L.acoustic_wave_propagation -> L.us_transmit_beam -> L.us_pulse_echo -> L.transducer_detection_dual -> int.spectral_temporal_spatial

L.optical_sourceL.optical_diffusionL.beer_lambertL.thermoelastic_grueneisenL.acoustic_wave_propagationL.us_transmit_beamL.us_pulse_echoL.transducer_detection_dualint.spectral_temporal_spatial

Well-posedness W

Existence:: true
Uniqueness:: conditional
Stability:: conditional
κ:: 280

Existence of recovered joint state (mu_a, Z, c, rho) is guaranteed within the declared Omega bounds. Uniqueness holds under multi-illumination + multi-wavelength PA acquisition combined with US transmit-receive at adequate SNR; single-wavelength single-illumination PAUS suffers the same multiplicative non-uniqueness as single-wavelength qPAT (excluded from the spec range). Stability is moderately conditioned (kappa_eff ~ 40 after joint model-based reconstruction) — pa_us_synchronization_jitter dominates registration error; fluence_inhomogeneity dominates qPAT-class chromophore bias; acoustic_attenuation dominates US-class deep-tissue contrast; transducer_bandwidth_difference_pa_vs_us contributes a frequency-dependent reconstruction artifact (PA typically lower-frequency band 0.5-10 MHz, US higher 5-20 MHz). Joint Hadamard well-posedness for the coupled qPAT + US Born forward is established by the qPAT references (Bal-Uhlmann 2010, Bal-Ren 2011) plus the dual-mode literature: Niederhauser et al. 2005 (combined OAT/US), Beard 2011 (review), Wang LV 2008 (multiscale photoacoustic), Mehrmohammadi et al. 2013 (PA-US clinical), Park et al. 2017 (PAUS guided interventions).

Solvability C

Solver class:: linear-operator + convex optimisation [joint qPAT + US ML reconstruction; alternating PA/US blocks with shared tissue model; FEM-based unified forward] | model-based iterative [k-Wave + Field II coupled solver] | linear-operator + deep neural prior [PAUS-Net dual-encoder]
Convergence rate q:: 2
Complexity:: O(H * W * Z * (N_PA_wavelengths + N_US_modes) * (transducer_count * time_samples)^(2/3)) per iteration via k-Wave + Field II coupled time-domain forward / adjoint; learned dual-encoder variants O(H W Z * F_theta_cost) per forward pass

Specs (0)

No L2 specs registered yet for this principle.