&lt;title&gt;Super-resolving image restoration in Karhunen-Loeve basis&lt;/title&gt;

Kurashov, Vitalij N.; Chumakov, A.G.; Kisil, Alexandr V.; Коваленко, А. В.

doi:10.1117/12.188062

Cited by 2 publications

(1 citation statement)

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“…Thus number of arithmetic operations for numerical processing or holographic filters number for coherent-optical treatment can be achieved. 4. The truncated KL representation provides not only minimal mean square error but effective filtration of white noise as a result of operator P1 action as well.…”

Section: Consideration Of a Priori Informationmentioning

confidence: 99%

<title>Image restoration by nonlinear mapping onto compact set</title>

Chumakov

Kurashov

1995

Nonlinear Image Processing VI

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We propose to solve the incorrect inverse problem of image restoration using the estimation of quasi-solution, which is the member of some optimized compact set. For such compact set we choose the subspace, which is spanned on the several first eigenvectors of symmetrized matrix CK=(CK+K*C)/2. Here C is an estimation of covanation of primary images, and K is (jseudo)inverse of noise covariation matrix. This representation provides concentration of noiseless images' energy in main spectral components and effective noise suppression under spectrum truncation. The non-orthogonal basic set for representation of distorted images was obtained from CK set by distortion operator. These two sets are used to compact matrix representation of distortion operator and its pseudo-inversion by singular decomposition procedure. We use the novel algorithm of training set decorrelation transformation for calculation of CK eigenvectors.In order to improve the restored image we use the iterative nonlinear procedure, which is based on influence function technique. Intermediate image is similar to primary distorted image, but with rough errors have been cleaned and omitted spots have been restored as well. A priori information about non-negative sign and limited variation of restored and intermediate images can easily be accounted. The proposed scheme of image processing enables restoration of large images with rough distortions in extremely high noise (up to 100%).We shall consider the restoration of image as process of inverse problem solution:Axy,xEX,yEY,where x is desired solution, y are known initial data, (distorted image), A is distortion operator, which reflects process of image formation. The operator A maps initial images set X to distorted images set V. Since known estimations of y and A have always some error, the solution x=A'y will be obviously approximate one. Usually even small errors in y and A lead to essential distortion of solution. In such cases the problem (1) is badly stipulated and should be regularized. It is possible if the problem is correct in Tikhonov's meaning. To be more specific, if for compact set X'cX the operator A is continuous, the regularizing operator R(a) can be found. The regularized solution x'=R(a)y is unique in X' and tend to exact one with decreasing of initial data error.The choice of set X' and operator R(x) is made due to a priori information about image and process of its formation. The better one use such information the more accurate solution can be obtained at certain value of initial data error. A priori information is formulated as a set of statements Sp. For example, S:"image counts are non-negative"; S11:"image energy doesn't exceed some value E"; S111:"the image is formed by linear system with the given function of point scattering" etc. The images x' for which statement S is correct, form some set X'pc.X. Generally speaking, some procedure itp of appropriate solutions selection and realizing it projection operator P exist. If some statements Sp are not invariant relatively to li...

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Section: Consideration Of a Priori Informationmentioning

confidence: 99%

<title>Image restoration by nonlinear mapping onto compact set</title>

Chumakov

Kurashov

1995

Nonlinear Image Processing VI

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<title>Pattern recognition with fast feature extraction</title>

1998

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The comparison ofrecently suggested algorithms of fast approximate Karhunen-Loeve(KL) transform when applied to pattern recognition problem is presented. It is known that adequate signs selection is stiff the problem. In the paper we consider several algorithms that can perform fast and quafltative signs selection. Among them are wavelet based algorithm of approximate XL transform, 2D algorithm ofKL transform. algorithm with projection into proper orthogoxialized basis, and real tinie algorithm ofKL transform. To compare quality ofthe algorithms they are apphed to human facts tecognition prob1m. Th evem'y of the all abovementioned algorithms is demonstrated.

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<title>Super-resolving image restoration in Karhunen-Loeve basis</title>

Cited by 2 publications

References 1 publication

<title>Image restoration by nonlinear mapping onto compact set</title>

<title>Image restoration by nonlinear mapping onto compact set</title>

<title>Pattern recognition with fast feature extraction</title>

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