{
  "abstract": "We propose a resolution-adaptive Bayesian wavelet denoising method for noisy one-dimensional signals. Its central innovation is a spike-and-slab prior whose continuous slab mixes a compactly supported Wendland-type polynomial density with the more dispersed semicircle density. A low-dimensional empirical-Bayes trend produces data-adaptive mixture weights by resolution, while a data-adaptive support scale controls the common bounded interval. Thus, the method combines sparsity, explicit support control, and interpretable resolution-dependent shrinkage. Under squared-error loss, we derive the posterior-mean estimator and establish symmetry, boundedness, continuity, and limiting properties. We define fixed-hyperparameter bias, variance, and risk and develop an empirical-Bayes fitting procedure. Under a Laplace working likelihood, the Wendland contribution has finite-sum expressions, while the semicircle contribution is evaluated by stable one-dimensional integration. Simulations with the Bumps, Blocks, Doppler, and HeaviSine signals compare Gaussian- and Laplace-likelihood versions with universal thresholding, false-discovery-rate (FDR) thresholding, cross-validation (CV), Stein's unbiased risk estimate (SURE), the Bayesian adaptive multiresolution shrinker (BAMS), and a nonlocal-prior (NLP) method. In the primary Gaussian-error study, WS--Gaussian was the best non-NLP method in 24 of 36 cells, including 11 of 12 low-SNR cells, with a much more favorable computational profile than WS--Laplace. A real seismic acceleration record from the 2008 Chino Hills earthquake illustrates attenuation of rapid fluctuations and preservation of the dominant event. A semi-synthetic study using the processed trace as surrogate truth showed improvement over the noisy observation at lower and moderate SNRs, but not at the highest SNR.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.03946",
  "author_total": 1,
  "authors": [
    {
      "name": "Nilotpal Sanyal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/953zn1kcdrn66.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.03946",
  "fulltext_url": null,
  "id": "953zn1kcdrn66",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.03946",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1707|Image and Signal Denoising Methods"
    ]
  ],
  "openalex": "W7172510318",
  "pdf_url": "https://arxiv.org/pdf/2608.03946",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/953zn1kcdrn66.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:54Z",
      "native_id": "2608.03946",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.03946"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Resolution-Adaptive Compact-Support Priors for Bayesian Wavelet Denoising",
  "title_text": "Resolution-Adaptive Compact-Support Priors for Bayesian Wavelet Denoising",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:54Z",
  "url": "https://research.draconitic.com/paper/953zn1kcdrn66",
  "venue": "arXiv",
  "versions": []
}