When Magnitude Suffices: Reconstructing Time-Domain-Gated Microwave Signals Without Phase on a Thoracic Phantom

Maciej Cichoń; Patrycja Gołaś; Maksymilian Bartosik; Angelika Walczak; Agata Bielecka-Dąbrowa; Maciej Ślot

cs.LGOct 16, 2026

When Magnitude Suffices: Reconstructing Time-Domain-Gated Microwave Signals Without Phase on a Thoracic Phantom

Authors: Maciej Cichoń, Patrycja Gołaś, Maksymilian Bartosik, Angelika Walczak, Agata Bielecka-Dąbrowa, Maciej Ślot

Organizations: Department of Solid State Physics, Faculty of Physics and Applied Informatics, University of Łódź, Pomorska 149/153, 90-236 Łódź, Poland · Polish Mother’s Memorial Hospital Research Institute, Rzgowska 281/289, 93-338 Łódź, Poland

Abstract

Time-domain gating separates the arrivals that form a microwave S-parameter measurement. It requires the measurement of complex values, so this application almost always uses a vector network analyzer (VNA). We show that, on one calibrated measurement configuration, the gated magnitude the VNA would give can be reconstructed from a magnitude-only sweep of a spectrum analyzer with a tracking generator (SA). We select the gate center for separability of the measured states, correct each instrument once by a per-bin subtraction of a reference state, and train a fully connected network on sweeps from both instruments. The test object is a torso phantom with lung-shaped compartments whose filling takes eleven dielectric states, each held out in turn. On $S_{11}$ the reconstruction from SA input reaches a shape error of 0.08 dB $^2$ with a state ordering of 0.81. This matches the reconstruction from VNA input. On $S_{21}$ it reaches 0.82 dB $^2$ and keeps the ordered groups of the states. An explicit phase prediction performs much worse, because gating needs the phase to about 0.2 rad RMS. Across eleven measurement configurations the dependence of phase on magnitude is strong for reflection and weak for transmission. This explains the difference between $S_{11}$ and $S_{21}$ . Where the magnitude carries enough of the phase, a scalar instrument gives the gated response without any phase measurement after installation. On the open UM-BMID breast data set, with whole phantoms held out, the shape error of the network is 30 percent lower than that of a per-bin linear map.

Figures & tables

Fig. 1: Measurement phantom and setup. (a) Schematic of the phantom, top view. (b) Prepared measurement phantom, top view. (c) Measurement system, side view. (d) Lung-shaped compartments with positioning elements.

Step	Exchanged (mL)	$\varepsilon^{\prime}$ at 2 GHz
0	0	78.0
1	100	72.9
2	200	68.4
3	300	64.5
4	400	61.0
5	500	58.0

Table 1: Lung-compartment filling steps and nominal real permittivity at 2 GHz.

Fig. 2: $S_{21}$ , gated shape error when the true magnitude is gated with a substitute phase, against gating with the true phase. The dashed line marks the direct magnitude-to-gated model at its within-VNA median over the held-out states.

Fig. 3: $S_{11}$ , gated shape error when the true magnitude is gated with a substitute phase, against gating with the true phase, as in Fig. 2 . The dashed line marks the direct magnitude-to-gated model at its within-VNA median over the held-out states (0.017 dB 2 ).

Fig. 4: $S_{11}$ per-state means. The left panel is the VNA-gated target; the right panel is the reconstruction from SA input with the full method (training on both instruments, ordering loss, smoothed).

Fig. 5: $S_{21}$ per-state means, same display as Fig. 4 . The three groups of dielectric states and their order are preserved across the change of instrument.

Fig. 6: $S_{21}$ per-state means, same display as Fig. 5 ; VNA-gated target left, reconstruction from SA input under training on VNA sweeps only right, ordering $-0.01$ .

Fig. 7: $S_{11}$ per-state means, same display as Fig. 4 ; VNA-gated target left, reconstruction from SA input under training on VNA sweeps only right, ordering 0.59.

S-param.	Training	VNA shape	VNA $\rho$	SA shape	SA $\rho$
$S_{11}$	VNA only	0.037	0.90	0.243	0.59
$S_{11}$	both, plain loss	0.047	0.87	0.076	0.82
$S_{11}$	both, ordering loss	0.047	0.88	0.082	0.81
$S_{21}$	VNA only	0.052	0.86	0.78	$-0.01$
$S_{21}$	both, plain loss	0.069	0.84	0.99	0.25
$S_{21}$	both, ordering loss	0.061	0.86	0.82	0.28

Table 2: Results with one dielectric state held out at a time. Shape error in dB 2 and ordering as Spearman

\rho

, evaluated on VNA input and on SA input. The plain loss is per-bin mean-squared error alone.

Method	0.5 ns gate	1.0 ns gate	Ordering $\rho$
reference curve	8.7	13.1	$-0.8$
per-bin linear map	2.5	4.6	1.0
network (this work)	1.8	3.8	1.0
minimum phase, then gate	67	66	$-0.8$
stored reference, learned quadrature, then gate	2.2	4.6	1.0

Table 3: Open breast data set with whole phantoms held out. Median shape error in dB 2 of the held-out sweeps of UM-BMID generation two, five folds over 66 phantoms, for two gate widths. Ordering of the four density classes as Spearman

\rho

at the 0.5 ns gate.

S-param.	Regime	$n$	dCor	CV $R^{2}$
$S_{11}$	within (1 config.)	275	1.00	0.95
$S_{11}$	across, combined	6776	0.83	0.97
$S_{11}$	across, mean removed	6776	0.56	0.86
$S_{21}$	within (1 config.)	275	0.75	0.64
$S_{21}$	across, combined	6776	0.68	0.52
$S_{21}$	across, mean removed	6776	0.60	0.47

Table 4: Magnitude-phase dependence. Distance correlation (dCor) and mean cross-validated

R^{2}

of phase on magnitude, with detrended phase. Rows per S-parameter: the single configuration; ten configurations combined; ten configurations combined with each configuration’s per-bin mean subtracted.

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Image Reconstruction from Phase with Untrained Neural Priors

Ene Meco, Ahmet Enis Cetin

Dept. of Electrical and Computer Engineering, University of Illinois at Chicago, IL, 60607, USA

Image Reconstruction Image Inverse Problems

Open paper AskPDF arXiv

Fourier phase encodes important spatial image structure, but recovering an image without measured spectral magnitude requires additional constraints and leaves absolute intensity ambiguous. We propose a projection-based two-stage framework that combines Fourier-phase and spatial-support constraints with an image-specific neural prior. The first stage alternates constraint enforcement with regularized neural-prior updates, while the second performs phase/support refinement alone with guaranteed convergence. We evaluate two neural-prior implementations on the same 77 microscopy images and compare them with a constraint-only baseline. After 500 final refinement passes, the best-performing variant achieves 31.41 dB pooled PSNR, 35.75 dB mean PSNR, and 0.9531 mean SSIM, improving pooled PSNR by 1.51~dB and reducing pooled MSE by 29.3% relative to the baseline. The results demonstrate the benefit of combining neural guidance with explicit constraint refinement at the evaluated iteration budget, while showing that lower phase residual alone does not guarantee greater reconstruction accuracy.

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