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Sparse Non-Negative Signal Recovery from Ill-Conditioned Blurred Observations

  • Task ID: math.nnls_modulus_deblur
  • Domain: math
  • Subdomain: numerical_linear_algebra
  • Status: final
  • Benchmark set: seed42 (60 tasks)
  • Tags: numerical-linear-algebra, nonnegative-least-squares, image-deblurring, ill-conditioned, sparse-inverse-problem, sparse-recovery, iterative-methods

Runtime and requirements

  • Estimated time: 45-90 minutes
  • Python: >=3.11
  • Packages: numpy>=1.26, scipy>=1.11, matplotlib>=3.8, Pillow>=10.0
  • GPU required: no
  • Network required: no

Public input and output contract

Inputs

  • observation.npy (data): Noisy, blurred observation b of shape [H, W], float64.
  • kernel.npy (data): Spatially invariant convolution kernel h of shape [H, W], float64. Energy is concentrated near the center (index H//2, W//2) with zeros elsewhere. Apply the forward operator A via circular FFT convolution using H_spectrum = fft2(ifftshift(h)); then A x = real(ifft2(H_spectrum * fft2(x))). Under this convention the kernel support size is an informational property of the PSF shape, not a constraint on the file shape.
  • measurement_info.json (data): Sidecar metadata containing image_shape and noise_std_estimate only. No methodological hints, no condition number, no sparsity information.

Outputs

  • solution.py (code): End-to-end Python implementation produced by the agent. Scanned by a quality-gated code-analysis scorer.
  • reconstruction.npy (data): Recovered non-negative signal x_hat, shape [H, W], float64.
  • reconstruction.png (figure): Three-panel visualization: observation | reconstruction | |observation - A*reconstruction|.
  • iteration_log.csv (data): Per-step iteration log. Required columns (in this exact order): step,residual_norm,complementarity. Must contain at least 10 rows. Column header line required.
  • metrics.json (data): Agent-reported diagnostics: final_residual, nonneg_violation_count, iterations_used, and an optional self-estimated relative error.

Public repository files

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Provenance

This task is included in the current seed42 benchmark set at dataset revision f11a199f71fb4b854ac43a1bf548d5df519141a9.

This page is generated only from files tracked in the public ASI-Bench repository at commit f18382f03faf. Submission bundles, run logs, private scoring configuration, and private reference answers are not read by this page generator.