Significance Moving infrared small target detection is important for infrared search and tracking, early warning, precision guidance, airspace surveillance, maritime monitoring, and remote sensing. The task aims to detect tiny, low-contrast targets with weak texture and semantic information from continuous infrared sequences. Compared with single-frame detection, sequence-based detection must also handle target displacement, platform jitter, background motion, motion blur, and unstable target responses across frames. These factors change target appearance and frame-to-frame correspondence and make weak targets more easily confused with background clutter and sensor noise. Temporal information can strengthen weak target evidence, but incorrect temporal association can also accumulate errors. A clear framework is still needed to explain how different methods use motion and temporal information and to compare optimization-driven and deep learning methods under different evaluation settings.

Progress A two-route taxonomy was established to organize recent moving infrared small target detection research. The first route is optimization-driven detection, and the second is deep learning-based detection. Optimization-driven and deep learning fusion is treated as a connecting direction between the two routes rather than as an additional optimization branch. This organization highlights both the main methodological split and the gradual interaction between explicit model priors and learned representations.

Optimization-driven methods are grouped into three branches according to the main stage they improve. Spatio-temporal tensor structure design reorganizes sequence data to strengthen useful spatial and temporal correlation before optimization. Low-rank background representation uses improved low-rank models, factorized representations, coefficient modeling, and graph constraints to describe complex backgrounds more accurately and reduce decomposition cost. Target-interference separability constraints go beyond a single sparsity assumption and use structural, directional, and saliency information to distinguish real targets from target-like background residuals. The three branches therefore focus on data organization, background representation, and target-background separation, respectively. Their common strengths are clear physical meaning and low dependence on detection annotations. Their main limitations are sensitivity to prior assumptions, parameter settings, tensor construction, and iterative computation.

Deep learning methods are also grouped into three branches according to how temporal information is represented and used. Explicit motion cue-guided spatio-temporal fusion uses registration, temporal differences, optical flow, direction coding, deformable sampling, dynamic queries, or motion-aware adaptation to guide cross-frame feature aggregation. Its development shows a shift from input-level motion correction to feature-level compensation, long-range matching, motion-sensitive operators, and adaptation of pretrained visual models. Inter-frame correlation-based temporal feature fusion does not require a complete physical motion field. It estimates similarity between frames or candidate locations and selects useful information through attention or correlation search. This route offers flexible cross-frame association, but large search regions can introduce unrelated candidates and extra computation. Implicit temporal representation and feature modeling stores sequence information in recurrent states, memory, state-space representations, temporal profiles, or background evolution models. It extends temporal use from short-term accumulation to longer-term dynamic modeling, but long sequences may mix useful evidence with outdated or irrelevant information and may weaken direct spatial correspondence.

The interaction between the two main routes has produced several fusion forms. Fusion methods insert learned denoisers into optimization, use untrained networks as implicit priors, constrain neural representations with model knowledge, unfold iterative optimization into trainable networks, or use mathematical motion models to organize temporal information in end-to-end detectors. These approaches differ in where model knowledge is introduced, whether offline training is required, and whether inference still needs per-sequence optimization. They show that the key issue is not simply choosing model knowledge or data learning, but assigning each of them an appropriate role in the detection process.

Evaluation methods were also reviewed together with computational efficiency. Current studies use pixel-, target-, box-, and response-map metrics together with accuracy, false-alarm, complexity, and speed measures. Direct comparison remains difficult because optimization methods and deep networks may output response maps, masks, heatmaps, or boxes. Data splits, input frame numbers, temporal sampling, image resolution, preprocessing, matching rules, hardware, and runtime reporting are also inconsistent. Existing benchmark efforts improve reproducibility within specific method families, but a common evaluation protocol covering optimization-driven, deep learning, and hybrid methods is still incomplete.

Conclusions and Prospects The reviewed literature shows that moving infrared small target detection has developed along two main routes with three major branches in each route, while Optimization-driven and deep learning fusion increasingly connects them. This taxonomy shows that progress is not a single network evolution path, but a joint development of sequence organization, background modeling, target-interference separation, motion guidance, cross-frame association, and temporal representation. Future work should first improve common evaluation protocols so that different output types and method families can be compared under consistent data splits, sequence sampling, input size, matching rules, false-alarm statistics, preprocessing, and complete runtime reporting. Target motion should be better separated from platform and background motion, with reference-frame quality and matching confidence used to reduce error accumulation. Dataset development and cross-scene generalization should be considered together by adding high-speed and irregular motion, occlusion, low signal-to-clutter ratios, platform disturbance, sensor variation, and realistic imaging degradation, while learning spatial and temporal features that are less tied to a particular sensor or dataset. Real-time evaluation should cover the full temporal processing pipeline rather than network forward time alone and should encourage feature reuse, adaptive temporal ranges, sparse sampling, and lightweight refinement. Fusion methods should further estimate when low-rank, sparse, smoothness, or motion-continuity assumptions are reliable and adjust their influence according to scene changes. Finally, weakly supervised, semi-supervised, self-supervised, and lightweight pretrained-model adaptation should make better use of unlabeled infrared video and combine general visual knowledge with infrared local structure and motion information. Together, these efforts may improve evaluation consistency, reduce annotation dependence, strengthen robustness under unseen conditions, and support more reliable deployment.