Add TV/polar-TV, trust-gating, edge-guard, HV_polar misfit and VE precompute (new enhanced script)

[Fuwsusu]

Motivation

• Reduce concentric ring artifacts and high-frequency center→edge contamination by adding directional regularizers and high-frequency guards.
• Improve robustness of frequency-domain waveform inversion to interpolation/virtual-element errors via per-frequency VE precomputation and channel-weighting.
• Increase misfit convexity and phase robustness by introducing an HV_polar phasor decomposition for separate amplitude/phase treatment.
• Provide runtime diagnostics and adaptive control (trust gate, step damping, lambda adjustments) to avoid steps that increase misfit or ring metrics.

Description

• Implemented isotropic Huber-TV (enableTV, lambda_tv, eps_tv) and a polar/radial TV (enablePolarReg, lambda_polar, eps_polar_reg) with relative normalization and added them into the gradient pipeline.
• Added high-frequency trust gating and adaptive controls (enableTrustGate, phi_small_drop_ratio, alpha_gate_*, lambda_polar_gate_*) that scale step sizes and radial-TV when data-consistency and ring metrics indicate risk.
• Added outer-edge protection (enableEdgeGuard, lambda_edge_anchor, edge_step_damp_max, edge_blend_*) that anchors outer ring to low-frequency reference and damps updates on the periphery; implemented masks (ring_bg_mask, edge_guard_mask) and contamination metrics used by the gate.
• Implemented HV_polar misfit (amplitude/phase decomposition) with per-pass phase weight (alpha_hv/alpha_hv_atten), channel confidence weighting for virtual receivers (beta_ve), illumination preconditioning (enableIllumComp), three-stage low-frequency prior saving/apply (enableLFPrior, VEL_stage1_ref, VEL_stage2_ref), and a per-frequency VE precompute with two frac-shift variants; added a new file MultiFrequencyWaveformInvkWave_fws20260409_2.m containing the full enhanced script.
• Added runtime diagnostics and iteration history storage: PHI_ITER, DELTA_PHI_ITER, TAU_SHIFT_ITER, R_RING_ITER, GAMMA_TRUST_ITER, ALPHA_GATE_ITER, LAMBDA_POLAR_EFF_ITER, LAMBDA_EDGE_EFF_ITER, EDGE_* arrays and saved them into the results .mat for post-analysis.
• Performance/UX tweaks: pre-create GIF figure and reuse image handle (saveGIF logic) and restrict scaling to real receivers when computing scaling to avoid virtual-Rx bias.

Testing

• No automated tests were run as part of this PR.

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Codex Task