TF-DETR: Patch-Constrained Set Prediction for Patch-wise Interval Estimation of Nonstationary Multi-Sinusoid Components

We propose TF-DETR, an end-to-end method that simultaneously estimates, for each component in a nonstationary multi-sinusoid signal, its existence interval (onset/offset) and continuous parameters {frequency, amplitude, phase}, together with a componentness score. In query-based set prediction with one-to-one bipartite matching, the number of near-tiesassignment candidates with nearly identical costs-increases under multi-component and closely spaced conditions, which can induce misassignments and training instability. TF-DETR introduces patch-constrained set prediction that localizes the decoder and matching within each time patch, thereby reducing competition density and the search space, and structurally enlarging the matching margin to mitigate near-ties. Because phase depends on the segmentation (cropping) origin, we regress it in a patch-referenced manner, while frequency and amplitude are estimated at the center time of each patch and concatenated over time to form ridges on the time-frequency plane. On a synthetic dataset, TF-DETR improves Recall@0.5 from 0.67 to 0.90 in the baseline setting and reduces the [0,1]-normalized MAE from 0.0053 to 0.0026 (frequency), 0.053 to 0.027 (amplitude), and 0.046 to 0.015 (phase). Relative gains are also confirmed across SNR conditions (white/colored noise), frequency bands, and high-density settings.