{
  "id": "1404.4774",
  "version": "v2",
  "published": "2014-04-18T12:51:24.000Z",
  "updated": "2014-09-30T03:29:44.000Z",
  "title": "Image Denoising with a Unified Schattern-$p$ Norm and $\\ell_q$ Norm Regularization",
  "authors": [
    "Jing Wang",
    "Meng Wang",
    "Xuegang Hu",
    "Shuicheng Yan"
  ],
  "comment": "This paper has been withdrawn by the authors. We found some mistakes in our experiments as some guys contacted us and they have read the paper from arXiv. So we believe this is very important and critical to withdraw the article as soon as possible, as we cannot present new experiments in a short time. We'd like to withdraw it. If arXiv cannot withdraw the paper as soon as possible, this article may degrade the reputation of arXiv. Thank you",
  "categories": [
    "cs.CV"
  ],
  "abstract": "Image denoising is an important field in image processing since the common corruption in real world data. In this paper, we propose a non-convex formulation to recover the authentic structure from corrupted data. Typically, the specific structure is assumed to be low rank, which holds in a wide range of data, such as image and video. And the corruption is assumed to be sparse. In the literature, such problem is known as Robust Principle Component Analysis (RPCA), which usually recovers the low rank structure by approximating the rank function with a nuclear norm and penalizes the error by $\\ell_1$-norm. Although RPCA is a convex formulation and can be solved effectively, the introduced norms are not tight approximations, which may deviate the solution from the authentic one. Therefore, we consider here a non-convex relaxation, consisting of a Schattern-$p$ norm and an $\\ell_q$-norm that promote low rank and sparsity respectively. We derive a proximal iteratively reweighted algorithm (PIRA) to solve the problem. Our algorithm is based on alternating direction method of multipliers, where in each iteration we linearize the underlying objective function that allows us to have a closed form solution. We demonstrate that solutions produced by the linearized approximation always converge and have a tighter approximation than the convex counterpart. Experimental results on benchmarks show encouraging results of our approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-18T12:51:24.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-30T03:29:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "image denoising",
      "norm regularization",
      "robust principle component analysis",
      "promote low rank",
      "real world data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.4774J"
    }
  }
}