GPU-Accelerated Matrix-Based Hough Transform for Online Track Reconstruction in the STCF MDC

Abstract: The Super Tau-Charm Facility (STCF) is a proposed next-generation high-luminosity electron-positron collider operating at center-of-mass energies of 2-7 GeV for precision studies of tau-charm physics. Its high event rate, detector occupancy, and background level impose stringent requirements on real-time track reconstruction in MDC, particularly for low-transverse-momentum particles with strongly curved or multi-turn trajectories. To address this challenge, we develop a GPU-accelerated matrix-based Hough transform method for online track reconstruction in the STCF MDC. Following an algorithm-architecture co-design paradigm, the data representation and computational workflow of the conformal Hough transform are reformulated for GPU execution. The original irregular parameter-space computations are organized into regular matrix-based operations, and the core computations are adapted to CUDA thread organization and the GPU memory hierarchy to exploit the inherent parallelism of the Hough transform and reduce computational and data-transfer overhead. Tests on five representative simulated physics channels with nominal background overlay show an average signal retention ratio of 93.04%, while reducing the retained hit volume to 34.92% of the original level. The GPU implementation processes 1,000 events in approximately 0.14s, achieving a speedup of 151.57 x compared with the CPU baseline. These results demonstrate that the proposed method substantially improves track reconstruction throughput while preserving track-associated hits, providing a new methodological perspective for real-time track reconstruction in future high-luminosity particle-collider experiments.

• The paper introduces a GPU-accelerated, matrix-based Hough transform that leverages conformal transformation to simplify circular track detection in the STCF MDC.
• It reformulates traditional Hough routines into dense matrix operations, achieving a 151.57x speedup and a 93.04% signal retention ratio over CPU methods.
• The approach demonstrates effective background hit suppression and scalability for real-time processing in high-luminosity collider environments.

GPU-Accelerated Matrix-Based Hough Transform for Online Track Reconstruction in the STCF MDC

Overview and Motivation

The Super Tau-Charm Facility (STCF), a high-luminosity electron-positron collider proposed for the 2–7 GeV center-of-mass energy regime, presents unique demands for the data acquisition and trigger systems, particularly in the context of online track reconstruction within the Main Drift Chamber (MDC). The high event rate and elevated detector occupancy, especially in scenarios with significant electronic noise and beam-induced backgrounds, render conventional CPU-based combinatorial or iterative tracking methods infeasible due to latency and throughput constraints. Robust, low-latency track reconstruction algorithms capable of efficiently filtering signal from overwhelming background are critical to downstream data compression, filtering, and physics analysis.

In this context, the paper proposes a GPU-accelerated, matrix-based Hough transform algorithm, designed with explicit attention to algorithm-architecture co-design, for high-throughput online track reconstruction in the STCF MDC. The central innovation is the reformulation of the Hough transform routines into dense, regular matrix operations compatible with GPU parallelism, supplanting irregular memory access patterns and atomic contention issues that typically hinder Hough-based approaches in real-time high occupancy environments.

Technical Approach

Parameter-Space Reformulation and Conformal Transformation

Charged-particle track reconstruction in the transverse plane is naturally formulated as a search for circular arcs, leading to high-dimensional parameter spaces if tackled directly. This work applies a conformal transformation $(x,y)\rightarrow(u,v)$ whereby circles through (or near) the origin are mapped to straight lines, simplifying track search to a line detection problem in transformed space. The Hough transform is then performed in the $(p, \theta)$ parameterization, discretizing the parameter space into a $1000 \times 1000$ regular grid, thus ensuring a deterministic mapping and enabling efficient data-parallel operations.

Matrix-Based Algorithm Structure

Rather than updating a shared accumulator through serial nested loops (which suffer from substantial branching, random access, and atomic update contention on GPUs), the core computation of the Hough transform—mapping hits to parameter space, voting accumulation, and local maximum search—is recast as matrix multiplications and column-wise reductions. Angular samples are partitioned along the $\theta$ dimension; each angle column is handled independently in a thread block. CUDA-optimized kernels are structured such that:

• Each event's hits are transformed and parameter-mapped in parallel along angular columns.
• Accumulator updates are performed with minimized atomic operations and optimized shared memory usage.
• Peak finding and non-maximum suppression are performed on-device, returning only candidate-parameter results to the host.
• Batch event-level and within-event parallelism are exploited via multi-thread and multi-block scheduling.

Such a decomposition substantially improves GPU resource utilization and amortizes fixed data transfer and kernel launch overheads across large event batches.

Experimental Evaluation

Physics Performance

The implementation was tested on five representative physics channels, with both signal retention and data compression ratios used as metrics:

• Signal retention ratio (proportion of true hits retained after filtering) averaged 93.04% across channel tests.
• Data compression ratio (retained candidate hits vs. total hits) averaged 34.92%, indicating that the majority of redundant hits are discarded, reducing input size for downstream fitting.
• Transverse-momentum and azimuthal-angle residuals demonstrated minimal systematic bias; for transverse-momentum, the relative residual distribution centered at $-0.0187$ with standard deviation $0.0528$. For azimuthal angle, the Gaussian width was $28.8$ mrad. Non-Gaussian tails in angle residuals for low-$p_T$ tracks were attributed to reconstruction ambiguities for tracks with large curvature or multi-turn topologies, not calibration bias.
• Track reconstruction efficiency exceeded 0.9 for the full tested $p_T$ range, demonstrating robustness to variations in track curvature and event topology.

Computational Scaling and Throughput

• The GPU implementation on an RTX 5060 Ti achieved processing of 1,000 events in 0.14 s, corresponding to an average per-event runtime of 0.14 ms.
• Comparative studies indicate a speedup of 151.57x over the CPU matrix-based baseline. Increases in event batch size led to sublinear runtime growth on the GPU, demonstrating high scalability and effective parallelization of independent tasks.
• Analysis of kernel performance revealed that the Hough voting step is the most sensitive to thread-block sizing; moderate block sizes yielded optimal performance, balancing occupancy and resource contention.

Robustness and Applicability

The approach demonstrates strong suppression of background hits while retaining the majority of true tracks for primary-vertex-centric events. Performance deteriorates for tracks originating from secondary vertices—due to intrinsic limits of Hough parameter-space mapping for tracks not matching the primary-vertex constraint—but remains effective for the dominant physics topologies in STCF.

Implications and Future Directions

The matrix-based, GPU-optimized Hough transform establishes a practical methodology for online real-time track reconstruction in high-luminosity collider experiments. The explicit realignment of algorithmic design with architectural features of modern GPUs overcomes historic limitations of Hough-based trigger algorithms in high-occupancy environments.

Future work outlined includes:

• Adaptive parameter-space partitioning and dynamic peak-thresholding, to better accommodate secondary-vertex and multi-turn topologies.
• Integration with fast Kalman filtering for candidate refinement, hit association, and parameter estimation corrections.
• Exploration of asynchronous, multi-GPU, and pipeline-parallel CUDA features to further improve processing throughput and resource utilization, targeting future upgrades of the STCF and similar facilities.

These directions align with broader trends in real-time heterogeneous computing for high-energy physics, where efficient algorithm-hardware co-design is increasingly central.

Conclusion

By leveraging a conformal transform and matrix-based restructuring of the Hough transform within a GPU-capable paradigm, this work achieves substantial improvements in both physics fidelity and computational throughput for online track reconstruction in the STCF MDC. The demonstrated speedup and stable reconstruction quality across multiple channels and event rates validate the approach as a viable candidate for high-luminosity HLT systems. Theoretical and practical extensions, including adaptive parameterization and multi-stage candidate refinement, will further increase resilience and efficiency in complex detector environments.

Reference: "GPU-Accelerated Matrix-Based Hough Transform for Online Track Reconstruction in the STCF MDC" (2607.04067)