[Paper Review] New algorithms for radio pulsar search

Kendrick M. Smith|arXiv (Cornell University)|Oct 21, 2016

Pulsars and Gravitational Waves Research3 citations

TL;DR

This paper introduces four new algorithms—optimal constant-period search, coherent tree search, semicoherent search, and hierarchical search—that drastically reduce computational cost in radio pulsar searches by leveraging recursive tree structures and phase-coherent signal combination. The methods achieve near-optimal detection with O(1) cost per model, reducing search complexity by orders of magnitude for large timestreams.

ABSTRACT

The computational cost of searching for new pulsars is a limiting factor for upcoming radio telescopes such as SKA. We introduce four new algorithms: an optimal constant-period search, a coherent tree search which permits optimal searching with O(1) cost per model, a semicoherent search which combines information from coherent subsearches while preserving as much phase information as possible, and a hierarchical search which interpolates between the coherent and semicoherent limits. Taken together, these algorithms improve the computational cost of pulsar search by several orders of magnitude. In this paper, we consider the simple case of a constant-acceleration phase model, but our methods should generalize to more complex search spaces.

Motivation & Objective

• Address the growing computational burden of pulsar searches in next-generation radio telescopes like SKA, where search space size scales poorly with timestream length.
• Overcome the limitations of traditional power-spectrum folding, which discards phase information and is suboptimal compared to coherent methods.
• Develop faster, near-optimal search algorithms that preserve phase coherence while reducing computational cost from O(S) to O(T) for large timestreams.
• Enable practical detection of faint pulsars by introducing scalable methods that interpolate between coherent and incoherent search strategies.
• Provide a framework adaptable to complex models such as polynomial phase models or binary pulsar systems, extending beyond constant-acceleration assumptions.

Proposed method

• Use a recursive tree algorithm to compute the optimal coherent overlap statistic for constant-acceleration models in O(1) cost per model, saturating the theoretical lower bound on computational cost.
• Implement a semicoherent search by dividing data into short coherent segments, computing coherent statistics per segment, and combining them via recursion that preserves phase information.
• Define a hierarchical search that progressively increases coherence time, allowing detection of pulsars whose phase models deviate from constant-acceleration at longer timescales.
• Apply recursion relations to the semicoherent statistic, enabling O(T) evaluation time despite an exponentially large search space in principle.
• Interpolate between coherent and semicoherent regimes by varying the coherence time Tc, allowing adaptive trade-offs between sensitivity and computational cost.
• Use the hierarchical structure to flag dropouts—candidates that are significant at short Tc but lose significance at longer Tc—indicating potential binary or non-constant-acceleration pulsars.

Experimental results

Research questions

• RQ1 Can we design a search algorithm that achieves near-optimal sensitivity for pulsars with constant-acceleration models while reducing computational cost from O(S) to O(1) per model?
• RQ2 How can phase information be preserved across multiple coherent segments to enable a semicoherent search with linear scaling in timestream length?
• RQ3 To what extent can a hierarchical search strategy detect pulsars that are poorly modeled by constant-acceleration or polynomial phase models?
• RQ4 Can the proposed methods be extended to higher-order phase models (e.g., degree 3–4 polynomials) with significantly reduced cost compared to full coherent searches?
• RQ5 How do the new algorithms compare in performance and robustness to RFI and false positives relative to traditional power-spectrum folding or incoherent stacking?

Key findings

• The recursive tree algorithm computes the optimal coherent overlap statistic for constant-acceleration models with O(1) cost per model, achieving the theoretical lower bound on computational cost.
• The semicoherent search method enables optimal detection for models with slowly varying acceleration, with computational cost scaling linearly as O(T) despite an exponentially large search space.
• The hierarchical search successfully identifies pulsars that deviate from constant-acceleration models by detecting statistical significance dropouts as coherence time increases.
• The full phase-coherent signal-to-noise ratio (Ŝ) is preserved in the hierarchical search, enabling robust false positive rejection by comparison to coherent detection thresholds.
• The methods are robust against weak, unmasked RFI, which tends to contribute incoherently and thus fails to mimic the sharply peaked likelihood of a true coherent pulsar signal.
• The proposed algorithms are expected to reduce computational cost by several orders of magnitude, making optimal pulsar searches feasible for large timestreams from next-generation telescopes like SKA and CHIME.