{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The wavelet domain is a sparse representation of the image, and can be thought of similarly to the frequency domain of the Fourier transform. Sparse representations have most values zero or near-zero and truly random noise is (usually) represented by many small values in the wavelet domain. Setting all values below some threshold to 0 reduces the noise in the image, but larger thresholds also decrease the detail present in the image." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If the input is 3D, this function performs wavelet denoising on each color plane separately." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "versionchanged", "base_type": "neutral", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "versionchanged 0.16" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "For floating point inputs, the original input range is maintained and there is no clipping applied to the output. Other input types will be converted to a floating point value in the range [-1, 1] or [0, 1] depending on the input image range. Unless " }, { "__type": "InlineCode", "__tag": 4051, "value": "rescale_sigma = False" }, { "__type": "Text", "__tag": 4046, "value": ", any internal rescaling applied to the " }, { "__type": "InlineCode", "__tag": 4051, "value": "image" }, { "__type": "Text", "__tag": 4046, "value": " will also be applied to " }, { "__type": "InlineCode", "__tag": 4051, "value": "sigma" }, { "__type": "Text", "__tag": 4046, "value": " to maintain the same relative amplitude." } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Many wavelet coefficient thresholding approaches have been proposed. By default, " }, { "__type": "InlineCode", "__tag": 4051, "value": "denoise_wavelet" }, { "__type": "Text", "__tag": 4046, "value": " applies BayesShrink, which is an adaptive thresholding method that computes separate thresholds for each wavelet sub-band as described in " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If " }, { "__type": "InlineCode", "__tag": 4051, "value": "method == \"VisuShrink\"" }, { "__type": "Text", "__tag": 4046, "value": ", a single \"universal threshold\" is applied to all wavelet detail coefficients as described in " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "2" }, { "__type": "Text", "__tag": 4046, "value": ". This threshold is designed to remove all Gaussian noise at a given " }, { "__type": "InlineCode", "__tag": 4051, "value": "sigma" }, { "__type": "Text", "__tag": 4046, "value": " with high probability, but tends to produce images that appear overly smooth." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Although any of the wavelets from " }, { "__type": "InlineCode", "__tag": 4051, "value": "PyWavelets" }, { "__type": "Text", "__tag": 4046, "value": " can be selected, the thresholding methods assume an orthogonal wavelet transform and may not choose the threshold appropriately for biorthogonal wavelets. Orthogonal wavelets are desirable because white noise in the input remains white noise in the subbands. Biorthogonal wavelets lead to colored noise in the subbands. Additionally, the orthogonal wavelets in PyWavelets are orthonormal so that noise variance in the subbands remains identical to the noise variance of the input. 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[1] Chang, S. Grace, Bin Yu, and Martin Vetterli. \"Adaptive wavelet", " thresholding for image denoising and compression.\" Image Processing,", " IEEE Transactions on 9.9 (2000): 1532-1546.", " :DOI:`10.1109/83.862633`", ".. [2] D. L. Donoho and I. M. Johnstone. \"Ideal spatial adaptation", " by wavelet shrinkage.\" Biometrika 81.3 (1994): 425-455.", " :DOI:`10.1093/biomet/81.3.425`" ], "qa": "skimage.restoration._denoise:denoise_wavelet", "arbitrary": [], "local_refs": [ "channel_axis", "convert2ycbcr", "image", "method", "mode", "out", "rescale_sigma", "sigma", "wavelet", "wavelet_levels" ] }