Single-objective perceptual losses for HDR phase-only CGH

A controlled search over 16 pure objectives and three difficulty axes. Final setting: 8 binary frames, 2×2 tied SLM logits, native ROI, original propagation and physical iris, 300 iterations, deterministic hard reconstruction.

Headline: reducing temporal frames alone makes L2-friendly speckle; narrowing the iris makes the task easier by low-pass denoising. Tying 2×2 SLM pixels creates the intended spatial resource bottleneck. Dense HDR encodings improve JOD modestly; pure structural metrics do not.

Choosing a genuinely harder task

1/2-frame mean L2 JOD: 7.933 / 8.815; native 4-frame: 9.355. A 0.75/0.5 iris unexpectedly raises L2 to 9.453/9.392, so it was rejected as a difficulty manipulation. A 2×2 tied SLM gives 7.772 at 4 frames and 8.099 at 8 frames.

Two batches of eight single losses

Batch A — pure structure: amplitude MS-SSIM, NLPD, MS-GMSD, HaarPSI; PU21-L1, PU21-MS-SSIM, PU21-NLPD; fixed exposure-stack MS-SSIM. These optimize stably but lose radiometric fidelity and JOD.

Batch B — dense perceptual encodings: sRGB-L2, amplitude Charbonnier, PU21-L2, PU21-Charbonnier, PQ-L2, μ-law(5000)-L2, HLG-L2, exposure-stack L2. Each is one transformed residual—not A+B and not an LR-only variant.

Dense objectiveBest LR (2-frame)2-frame JODSpatial-screen JOD
sRGB L20.18.6238.082
Exposure-stack L20.18.4968.111
PU21-L20.28.4698.148
PQ-L20.28.4418.153
Amplitude Charbonnier0.18.428—
HLG-L20.18.414—
PU21-Charbonnier0.18.332—
μ-law(5000)-L20.18.051—

12-scene, 300-iteration finalists

LossMean JODΔ vs tuned L2Mean PSNRMean SSIM
Amplitude L28.205+0.00023.840.5532
sRGB Charbonnier7.913-0.29223.700.5487
sRGB L28.268+0.06323.970.5532
PU21-L28.237+0.03223.590.5430

Hard reconstruction gallery

SceneAmplitude L2sRGB CharbonniersRGB L2PU21-L2
Toys8.413 JOD
26.89 dB · 0.670		8.302 JOD
26.87 dB · 0.667		8.519 JOD
27.11 dB · 0.665		8.673 JOD
26.83 dB · 0.659
Type7.565 JOD
19.57 dB · 0.289		7.269 JOD
19.56 dB · 0.287		7.617 JOD
19.70 dB · 0.288		7.647 JOD
19.43 dB · 0.280
Showgirl8.283 JOD
24.41 dB · 0.483		7.817 JOD
24.00 dB · 0.484		8.335 JOD
24.52 dB · 0.482		8.232 JOD
24.22 dB · 0.475
Lounge8.576 JOD
28.98 dB · 0.710		8.447 JOD
28.68 dB · 0.714		8.669 JOD
29.25 dB · 0.718		8.670 JOD
28.98 dB · 0.721
Rushmore7.903 JOD
22.10 dB · 0.486		7.338 JOD
21.93 dB · 0.477		7.971 JOD
22.28 dB · 0.484		7.968 JOD
22.10 dB · 0.472
Glade7.845 JOD
20.65 dB · 0.469		7.517 JOD
20.78 dB · 0.464		7.985 JOD
20.76 dB · 0.480		8.009 JOD
20.51 dB · 0.476
Snow9.181 JOD
30.59 dB · 0.822		9.136 JOD
30.22 dB · 0.823		9.232 JOD
30.75 dB · 0.825		9.182 JOD
30.10 dB · 0.817
Meridian8.393 JOD
23.82 dB · 0.547		8.098 JOD
23.70 dB · 0.546		8.433 JOD
23.88 dB · 0.547		8.426 JOD
23.37 dB · 0.544
Bloom8.081 JOD
19.37 dB · 0.553		7.856 JOD
19.43 dB · 0.550		8.157 JOD
19.51 dB · 0.552		8.162 JOD
19.40 dB · 0.544
Anime27.757 JOD
23.87 dB · 0.550		7.226 JOD
23.62 dB · 0.528		7.674 JOD
23.88 dB · 0.546		7.461 JOD
23.38 dB · 0.525
Water8.427 JOD
23.24 dB · 0.561		8.254 JOD
23.18 dB · 0.552		8.463 JOD
23.30 dB · 0.558		8.295 JOD
22.46 dB · 0.540
Castle8.034 JOD
22.59 dB · 0.497		7.700 JOD
22.45 dB · 0.494		8.156 JOD
22.66 dB · 0.493		8.117 JOD
22.25 dB · 0.463

Interpretation

The gain is real but not the requested +0.5 JOD. The spatial bottleneck reveals a useful distinction: dense monotonic HDR encodings retain the pixel accountability needed by Gumbel binary optimization, while pure similarity metrics can improve their own score by sacrificing absolute brightness. PU21/PQ help low-luminance Toys most but can hurt bright Water; sRGB-L2 is more consistent. This points to brightness-conditioned encoding as the next hypothesis, but the present report does not count per-scene oracle selection as a result.

Sources

Raw output: 2.79 GiB under /home/fy277/ph_opt_runs (10 GiB cap).