### Citations

3532 | A theory for multiresolution signal decomposition: The wavelet representation
- Mallat
- 1989
(Show Context)
Citation Context ...ncludes transforms (DCT, DWT, DFT, etc.), display strong super-Gaussian, i.e. kurt(x) > 0 (sharply peaked), characteristics. One illustration from the extensive collection of domain modeling includes =-=[5]-=-, which uses the wavelet detail domain. The histogram is modeled as X ∼ ξ0e−(|h(x)i|/α)β . (2) for any i where h(x)i is the ith wavelet detail coefÀcient. (2) results from independently distributed ch... |

115 | The Nonlinear Statistics of High-Contrast patches
- Lee, Pedersen, et al.
- 2003
(Show Context)
Citation Context ...roperties of the patches themselves, particularly focusing on their distribution. Anticipating the usefulness of such an investigation, especially when preprocessing in an input space, several papers =-=[1, 2, 3]-=- have explored this topic. The range of their investigations are diverse, but all of the studies eventually agree on some sort of high-dimensional manifold that cannot be easily explained. [1] assumes... |

43 |
On the multivariate Laplace distribution,”
- Eltoft, Kim, et al.
- 2006
(Show Context)
Citation Context ...hat kurt(u) = 3 in the univariate case. The behavior of multivariate Laplacian distributions is attractive because it belongs to a family of sparse distributionswhere there is a high peak at the mean =-=[7]-=-. Ignoring the extraneous terms that are unnecessary for our model, the distribution is deÀned in (7). L(x) = 2( 2π 1α ) d 2 ( xT x 2 ) 1 2− d4 I1− d2 (√ 2xT x α2 ) , (7) where Iλ denotes the modiÀed ... |

16 | The complex statistics of high-contrast patches in natural images. Private correspondence
- Lee, Pedersen, et al.
- 2001
(Show Context)
Citation Context ...roperties of the patches themselves, particularly focusing on their distribution. Anticipating the usefulness of such an investigation, especially when preprocessing in an input space, several papers =-=[1, 2, 3]-=- have explored this topic. The range of their investigations are diverse, but all of the studies eventually agree on some sort of high-dimensional manifold that cannot be easily explained. [1] assumes... |

11 |
Classification based methods in optimal image interpolation
- Atkins, Bouman
- 1998
(Show Context)
Citation Context ...s on the amount of information a single dimension can convey, which is augmented by most models’ almost universal zero-mean properties. Alternatively, patched-based applications, e.g. superresolution =-=[6]-=-, often model the overall distribution as a mixture of Gaussians (GMM). Rationalization behind such modeling is seldomly justiÀed in any imaging application, the mindset being more default than delibe... |

8 | Mapping natural image patches by explicit and implicit manifolds
- Shi
(Show Context)
Citation Context ...roperties of the patches themselves, particularly focusing on their distribution. Anticipating the usefulness of such an investigation, especially when preprocessing in an input space, several papers =-=[1, 2, 3]-=- have explored this topic. The range of their investigations are diverse, but all of the studies eventually agree on some sort of high-dimensional manifold that cannot be easily explained. [1] assumes... |

8 | Statistics of natural image geometry
- Pedersen
- 2003
(Show Context)
Citation Context ... appropriately scaling local statistics to correspond to a camera that zooms in on a particular scene. However, the extent of this effect is taken to be minimal, and given a sufÀciently large window, =-=[4]-=- suggests approximate scale invariance. That is, if I(x, y) be the observed image, then any given patch of I , patch(I(x, y)), approximately reÁects the statistics of patch(I(σx, σy)). An important me... |