[Paper Review] Algorithmic Optimisations for Iterative Deconvolution Methods

Martin Welk, Martin Erler|arXiv (Cornell University)|Apr 26, 2013

Sparse and Compressive Sensing Techniques12 references3 citations

TL;DR

This paper proposes two algorithmic optimizations to accelerate iterative non-blind deconvolution: (1) specialized convolution algorithms for common point-spread functions (PSFs) like box and defocus, and (2) selective convolution that restricts computation to pixels still changing during iterations. These methods reduce runtime by up to 5.27× with minimal impact on reconstruction quality, especially effective for spatial-domain deconvolution where Fourier transforms are avoided.

ABSTRACT

We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating these convolution operations as they are typically the most expensive part of the computation. We follow two approaches: First, for some practically important specific point-spread functions, algorithmically efficient sliding window or list processing techniques can be used. In some constellations this allows faster computation than via the Fourier domain. Second, as iterations progress, computation of convolutions can be restricted to subsets of pixels. For moderate thinning rates this can be done with almost no impact on the reconstruction quality. Both approaches are demonstrated in the context of Richardson-Lucy deconvolution but are not restricted to this method.

Motivation & Objective

• To reduce computational cost in iterative non-blind deconvolution methods where convolution with the PSF dominates runtime.
• To develop algorithmic optimizations that accelerate spatial-domain convolution without relying on Fourier transforms.
• To explore whether restricting convolution to only changing pixels in later iterations preserves reconstruction quality while reducing computation.
• To demonstrate that specialized convolution algorithms for common PSFs outperform FFT-based methods in specific cases.
• To evaluate the trade-off between speedup and image quality degradation in selective convolution approaches.

Proposed method

• For structured PSFs (e.g., box, defocus), implement optimized sliding window or list processing algorithms that compute convolution more efficiently than FFT-based methods.
• Use a threshold-based thinning strategy to skip convolution for pixels whose values have stabilized during iterations.
• Apply the selective convolution technique in the Richardson-Lucy deconvolution framework, updating only pixels where changes exceed a dynamic threshold.
• Implement boundary handling via reduced-domain convolution to avoid artifacts from missing data at image edges.
• Benchmark performance using SNR and runtime comparisons against standard FFT-based and full-convolution implementations.
• Use a 3 GHz CPU and average results over 100 runs to ensure statistical reliability of speedup and quality metrics.

Experimental results

Research questions

• RQ1 Can specialized convolution algorithms for common PSFs (e.g., box, defocus) outperform FFT-based convolution in terms of speed for spatial-domain deconvolution?
• RQ2 To what extent can selective convolution—limiting computation to only changing pixels—reduce runtime without degrading image quality?
• RQ3 How does the choice of thinning threshold affect the trade-off between computational speed and reconstruction fidelity?
• RQ4 Can these optimizations be applied beyond Richardson-Lucy deconvolution to other iterative deconvolution methods?
• RQ5 What is the maximum achievable speedup using these algorithmic optimizations while maintaining acceptable image quality?

Key findings

• For a 9-pixel diameter defocus PSF, the optimized box filter achieved a 5.27× speedup over standard FFT-based convolution with only a 1.08 dB drop in SNR compared to the reference.
• With a thinning threshold of 0.1, the method achieved a 2.75× speedup while preserving SNR within 0.2 dB of the reference, indicating minimal quality loss.
• At a threshold of 0.5, the speedup reached 5.27×, but SNR dropped to 12.23 dB, indicating visible degradation in image quality.
• The generic box filter outperformed FFT for all massive, convex 2D PSFs of constant density, while the list filter was most efficient for sparse PSFs.
• For PSFs of size 17×17, the FFT method was nearly on par with the generic box filter, indicating diminishing returns for larger kernels.
• The computational overhead of implementing selective convolution was less than 1%, confirming its practical feasibility.