[Paper Review] Fusion of Greedy Pursuits for Compressed Sensing Signal Reconstruction

Sooraj K. Ambat, Saikat Chatterjee+1 more|arXiv (Cornell University)|Apr 20, 2012

Sparse and Compressive Sensing Techniques12 references19 citations

TL;DR

This paper proposes a novel fusion framework, Fusion of Greedy Pursuits (FuGP), that combines orthogonal matching pursuit (OMP) and subspace pursuit (SP) to improve sparse signal recovery in compressed sensing. By fusing support sets from both algorithms and refining estimates via iterative feedback, FuGP and its improved variant IFuGP achieve significant performance gains—up to 252% SRER improvement over OMP in clean conditions and 196% in noisy regimes—especially in low-measurement and non-ideal signal scenarios.

ABSTRACT

Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical distribution of the non-zero elements in the sparse signal. In practice, the distribution of the sparse signal may not be known a priori. It is also observed that performance of Greedy Pursuits degrades as the number of available measurements decreases from a threshold value which is method dependent. To improve the performance in these situations, we introduce a novel fusion framework for Greedy Pursuits and also propose two algorithms for sparse recovery. Through Monte Carlo simulations we show that the proposed schemes improve sparse signal recovery in clean as well as noisy measurement cases.

Motivation & Objective

• Address the performance variability of greedy pursuit algorithms in compressed sensing due to unknown signal distribution and low measurement regimes.
• Overcome the limitation that individual greedy pursuits (e.g., OMP, SP) degrade significantly when measurements fall below a method-specific threshold.
• Develop a fusion framework that leverages complementary strengths of multiple greedy algorithms to improve robustness and accuracy in sparse signal reconstruction.
• Provide a signal-agnostic, adaptive recovery method that performs well across diverse signal types (Gaussian, Rademacher) and noise conditions without prior knowledge of signal statistics.

Proposed method

• Propose a fusion framework that combines the support sets of two greedy pursuit algorithms (e.g., OMP and SP) to form a union of candidate atoms.
• Introduce a two-stage reconstruction process: first, run OMP and SP independently to estimate partial supports; second, fuse these supports into a combined candidate set.
• Apply iterative feedback in the Improved FuGP (IFuGP) variant to refine the support estimate by re-evaluating residual energy and updating the solution iteratively.
• Use signal-to-reconstruction-error ratio (SRER) as the primary metric to evaluate performance across multiple Monte Carlo trials.
• Employ a randomized measurement matrix with normalized columns and generate sparse signals with i.i.d. Gaussian or Rademacher non-zero entries.
• Conduct simulations across clean and noisy measurement regimes (SMNR = 15 dB) with varying measurement fractions (α) to assess robustness and scalability.

Experimental results

Research questions

• RQ1 Can combining two greedy pursuit algorithms improve sparse signal recovery performance when the underlying signal distribution is unknown?
• RQ2 How does the fusion of OMP and SP support sets compare to individual algorithms in low-measurement regimes (α < 0.3)?
• RQ3 To what extent does the iterative refinement in IFuGP enhance reconstruction accuracy compared to the basic FuGP framework?
• RQ4 How robust are the proposed fusion methods in noisy measurement environments, particularly at SMNR = 15 dB?
• RQ5 Does the fusion framework consistently outperform individual greedy pursuits across different sparse signal models (Gaussian vs. Rademacher) and measurement conditions?

Key findings

• In clean measurement conditions with Gaussian sparse signals, FuGP achieved a 31% (6.5 dB) SRER improvement over OMP and a 58% (10 dB) improvement over SP at α = 0.18.
• For the same scenario, IFuGP(OMP, SP) achieved 59% (12 dB) and 91% (16 dB) SRER improvements over OMP and SP, respectively, with an additional 21% (5.72 dB) gain over FuGP.
• In noisy conditions (SMNR = 15 dB), FuGP improved SRER by 11% (1.1 dB) over OMP and 36% (3.1 dB) over SP at α = 0.18, while IFuGP further improved performance by 3% (0.35 dB) over FuGP.
• For Rademacher sparse signals in clean conditions, FuGP delivered a 203% (18 dB) SRER gain over OMP and 12% (2.8 dB) over SP at α = 0.25, with IFuGP achieving 252% (22 dB) and 30% (7 dB) improvements respectively.
• In noisy Rademacher cases, IFuGP achieved 196% (13.2 dB) and 16% (2.7 dB) SRER improvements over OMP and SP at α = 0.25, demonstrating strong robustness to noise.
• The proposed fusion framework consistently outperformed individual greedy algorithms across all signal types, measurement regimes, and noise levels, with IFuGP showing the most significant gains in low-α and noisy conditions.