[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/wiki40\/shrinkage-fields-image-restoration-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/wiki40\/shrinkage-fields-image-restoration-wikipedia\/","headline":"Shrinkage Fields (image restoration) – Wikipedia","name":"Shrinkage Fields (image restoration) – Wikipedia","description":"From Wikipedia, the free encyclopedia Shrinkage fields is a random field-based machine learning technique that aims to perform high quality","datePublished":"2015-03-25","dateModified":"2015-03-25","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/wiki40\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/wiki40\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/87f9e315fd7e2ba406057a97300593c4802b53e4","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/87f9e315fd7e2ba406057a97300593c4802b53e4","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/en\/wiki40\/shrinkage-fields-image-restoration-wikipedia\/","about":["Wiki"],"wordCount":5306,"articleBody":"From Wikipedia, the free encyclopediaShrinkage fields is a random field-based machine learning technique that aims to perform high quality image restoration (denoising and deblurring) using low computational overhead.The restored image x{displaystyle x} is predicted from a corrupted observation y{displaystyle y} after training on a set of sample images S{displaystyle S}.A shrinkage (mapping) function f\u03c0i(v)=\u2211j=1M\u03c0i,jexp\u2061(\u2212\u03b32(v\u2212\u03bcj)2){displaystyle {f}_{{pi }_{i}}left(vright)={sum }_{j=1}^{M}{pi }_{i,j}exp left(-{frac {gamma }{2}}{left(v-{mu }_{j}right)}^{2}right)} is directly modeled as a linear combination of radial basis function kernels, where \u03b3{displaystyle gamma } is the shared precision parameter, \u03bc{displaystyle mu } denotes the (equidistant) kernel positions, and M is the number of Gaussian kernels.Because the shrinkage function is directly modeled, the optimization procedure is reduced to a single quadratic minimization per iteration, denoted as the prediction of a shrinkage field g\u0398(x)=F\u22121[F(\u03bbKTy+\u2211i=1NFiTf\u03c0i(Fix))\u03bbK\u02c7*\u2218K\u02c7+\u2211i=1NF\u02c7i*\u2218F\u02c7i]=\u03a9\u22121\u03b7{displaystyle {g}_{mathrm {Theta } }left({text{x}}right)={mathcal {F}}^{-1}leftlbrack {frac {{mathcal {F}}left(lambda {K}^{T}y+{sum }_{i=1}^{N}{F}_{i}^{T}{f}_{{pi }_{i}}left({F}_{i}xright)right)}{lambda {check {K}}^{text{*}}circ {check {K}}+{sum }_{i=1}^{N}{check {F}}_{i}^{text{*}}circ {check {F}}_{i}}}rightrbrack ={mathrm {Omega } }^{-1}eta } where F{displaystyle {mathcal {F}}} denotes the discrete Fourier transform and Fx{displaystyle F_{x}} is the 2D convolution f\u2297x{displaystyle {text{f}}otimes {text{x}}} with point spread function filter, F\u02d8{displaystyle {breve {F}}} is an optical transfer function defined as the discrete Fourier transform of f{displaystyle {text{f}}}, and F\u02d8*{displaystyle {breve {F}}^{text{*}}} is the complex conjugate of F\u02d8{displaystyle {breve {F}}}.x^t{displaystyle {hat {x}}_{t}} is learned as x^t=g\u0398t(x^t\u22121){displaystyle {hat {x}}_{t}={g}_{{mathrm {Theta } }_{t}}left({hat {x}}_{t-1}right)} for each iteration t{displaystyle t} with the initial case x^0=y{displaystyle {hat {x}}_{0}=y}, this forms a cascade of Gaussian conditional random fields (or cascade of shrinkage fields (CSF)). Loss-minimization is used to learn the model parameters \u0398t={\u03bbt,\u03c0ti,fti}i=1N{displaystyle {mathrm {Theta } }_{t}={leftlbrace {lambda }_{t},{pi }_{mathit {ti}},{f}_{mathit {ti}}rightrbrace }_{i=1}^{N}}.The learning objective function is defined as J(\u0398t)=\u2211s=1Sl(x^t(s);xgt(s)){displaystyle Jleft({mathrm {Theta } }_{t}right)={sum }_{s=1}^{S}lleft({hat {x}}_{t}^{left(sright)};{x}_{gt}^{left(sright)}right)}, where l{displaystyle l} is a differentiable loss function which is greedily minimized using training data {xgt(s),y(s),k(s)}s=1S{displaystyle {leftlbrace {x}_{gt}^{left(sright)},{y}^{left(sright)},{k}^{left(sright)}rightrbrace }_{s=1}^{S}} and x^t(s){displaystyle {hat {x}}_{t}^{left(sright)}}.Table of ContentsPerformance[edit]Advantages[edit]Implementations[edit]See also[edit]References[edit]Performance[edit]Preliminary tests by the author suggest that RTF5[1] obtains slightly better denoising performance than CSF7\u00d77{3,4,5}{displaystyle {text{CSF}}_{7times 7}^{leftlbrace mathrm {3,4,5} rightrbrace }}, followed by CSF5\u00d755{displaystyle {text{CSF}}_{5times 5}^{5}}, CSF7\u00d772{displaystyle {text{CSF}}_{7times 7}^{2}}, CSF5\u00d75{3,4}{displaystyle {text{CSF}}_{5times 5}^{leftlbrace mathrm {3,4} rightrbrace }}, and BM3D.BM3D denoising speed falls between that of CSF5\u00d754{displaystyle {text{CSF}}_{5times 5}^{4}} and CSF7\u00d774{displaystyle {text{CSF}}_{7times 7}^{4}}, RTF being an order of magnitude slower.Advantages[edit]Results are comparable to those obtained by BM3D (reference in state of the art denoising since its inception in 2007)Minimal runtime compared to other high-performance methods (potentially applicable within embedded devices)Parallelizable (e.g.: possible GPU implementation)Predictability: O(Dlog\u2061D){displaystyle O(Dlog D)} runtime where D{displaystyle D} is the number of pixelsFast training even with CPUImplementations[edit]See also[edit]References[edit]^ Jancsary, Jeremy; Nowozin, Sebastian; Sharp, Toby; Rother, Carsten (10 April 2012). Regression Tree Fields \u2013 An Efficient, Non-parametric Approach to Image Labeling Problems. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). Providence, RI, USA: IEEE Computer Society. doi:10.1109\/CVPR.2012.6247950."},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki40\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki40\/shrinkage-fields-image-restoration-wikipedia\/#breadcrumbitem","name":"Shrinkage Fields (image restoration) – Wikipedia"}}]}]