CISTA-Net: Counting Matters for Closely-Spaced Infrared Small Target Unmixing

Closely-spaced infrared small target unmixing is an ill-conditioned inverse problem in which multiple sparse source configurations can produce highly similar observations under severe point-spread-function overlap. Existing deep unfolding methods adapt reconstruction parameters primarily from local or intermediate reconstruction features, but do not explicitly exploit scene-level source cardinality when deciding how aggressively sparse responses should be retained or suppressed. We investigate whether estimated target cardinality can serve as a global structural cue for iterative reconstruction, and instantiate this idea in CISTA-Net, a count-guided iterative shrinkage-thresholding network. CISTA-Net introduces a count-prior guided dynamic threshold generator (CP-DTG) that conditions stage-wise shrinkage on both local reconstruction features and a predicted count distribution. It further incorporates multi-stage image selective fusion (MSIF) to recover complementary intermediate responses and count-guided post-processing (CGPP) for count-consistent candidate selection. On CSIST-100K, CISTA-Net improves CSO-mAP over DISTA-Net from 46.74 to 47.28, 69.58 to 70.25, and 72.84 to 73.06 at sampling ratios \(c=3,5,7\), respectively, with the clearest gains under dense and moderately precise localization settings. These results suggest that explicit cardinality information provides complementary global guidance to locally adaptive deep unfolding.