Baselines¶

A baseline in nefi changes only the parameterization or the optimizer: the domain, the forward operator, the losses, the measurement and the post-processing stay identical, so a comparison isolates the prior. Every instance can run every baseline through nefi.baselines.baseline_problem; see Baselines for what each one means and when a comparison is fair.

Same data, six methods¶

Deconvolution: ground truth, blurred measurement and six reconstructions (neural field, ADMM, Deep Decoder, Gaussian splats, grid with TV, Wiener) with PSNR and SSIM, and their signed errors — `deconvolution`, phantom scene, 32², Gaussian PSF, 1 % noise, the same objective and budget for every iterative method (gallery run, CPU). The TV-regularized grid — the MAP estimate of this objective — is the strongest method on this well-conditioned linear problem; the neural field is close behind and well ahead of Wiener, the Deep Decoder, the Gaussian splats and ADMM.

method	PSNR [dB]	SSIM	parameterization
neural field	28.1	0.950	coordinate MLP + annealed Fourier features
grid + TV	29.1	0.971	free pixels (NeTMY "Tikhonov", NeFTY "Grid Opt.")
ADMM (ℓ1 + box)	25.2	0.810	splitting solver on pixels
Deep Decoder	24.1	0.876	untrained convolutional decoder
Gaussian splats	23.5	0.898	adaptive Gaussian primitives
Wiener	25.0	0.833	closed form

How each method fails¶

Failure modes of the six methods: reconstruction with the support outlined, signed error, mass leaking outside the support, and the log error spectrum — The same six reconstructions seen through their failure modes: signed error and relative error, the fraction of mass that leaks outside the true support (3.8 % for the neural field, 1.8 % for the grid, 7–12 % for ADMM, Wiener and the Deep Decoder), and the error spectrum (a cross-shaped excess would flag anisotropic artifacts).

When does the representation matter?¶

The ranking depends on the regime, and the documentation reports it either way:

Well-conditioned linear problems with an explicit prior (deconvolution, sparse-view CT with enough views, Poisson source): the TV grid is the MAP estimate of the objective and a very strong baseline; the neural field is competitive (deconvolution, sparse-view CT).
No explicit prior: the parameterization becomes the only regularizer. On deconvolution with 3 % noise and no TV, the neural field reaches 29.4 dB where the free grid fits the noise (23.0 dB) (Baselines § 4).
Missing data: in limited-angle 3-D CT the neural field wins on PSNR and structure (90° wedge: 24.9 dB / SSIM 0.78 against 23.7 dB / 0.62 for the grid) (ct3d).
Biased raw gradients: under NeTMY's tensor operator a free density collapses toward the center; the filtering kernel of the neural field is decisive (The representation is the prior).
Surface-only heat data: the voxel grid finds no defect (IoU 0) where NeFTY's neural field reaches IoU 0.97 on the same measurement (thermal tomography).

nefi run deconvolution --smoke --baseline grid                       # any baseline, one run
nefi bench deconvolution --smoke --methods neural,grid,admm,deep_decoder,gaussian_splat,wiener
python examples/baselines_comparison.py                              # the table in docs/baselines.md