Adaptive nonlinear image restoration by a modified Kalman filtering approach

An adaptive nonlinear Kalman-type filter is presented for the restoration of two-dimensional images degraded by general image formation system degradations and additive white noise. A vector difference equation model is used to model the degradation process. The object plane distribution function is partitioned into disjoint regions based on the amount of spatial activity in the image, and difference equation models are used to characterize this nonstationary object plane distribution function. Features of the restoration filter include the ability to account for the response of the human visual system to additive noise in an image; a two-dimensional interpolation scheme to improve the estimates of the initial states in each region; and a nearest neighbor algorithm to choose the previous state of vector for the state of pixel (i,j).

[1]  R. E. Graham,et al.  Snow removal-A noise-stripping process for picture signals , 1962, IRE Trans. Inf. Theory.

[2]  David L. Phillips,et al.  A Technique for the Numerical Solution of Certain Integral Equations of the First Kind , 1962, JACM.

[3]  S. Twomey,et al.  On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature , 1963, JACM.

[4]  S. Twomey.  The application of numerical filtering to the solution of integral equations encountered in indirect sensing measurements , 1965 .

[5]  L. Franks.  A model for the random video process , 1966 .

[6]  D. Slepian.  Linear Least-Squares Filtering of Distorted Images , 1967 .

[7]  C. Helstrom.  Image Restoration by the Method of Least Squares , 1967 .

[8]  A. Oppenheim,et al.  Nonlinear filtering of multiplied and convolved signals , 1968 .

[9]  David Pearce MacAdam,et al.  Digital Image Restoration by Constrained Deconvolution , 1970 .

[10]  Alberto Martelli,et al.  Optimal Smoothing in Picture Processing: An Application to Fingerprints , 1971, IFIP Congress.

[11]  Thomas S. Huang,et al.  Image processing , 1971 .

[12]  Jr. Thomas G. Stockham,et al.  Image processing in the context of a visual model , 1972 .

[13]  N. Nahi,et al.  Bayesian recursive image estimation. , 1972 .

[14]  Z. L. Budrikis,et al.  Visual fidelity criterion and modeling , 1972 .

[15]  William H. Richardson,et al.  Bayesian-Based Iterative Method of Image Restoration , 1972 .

[16]  Jr. Edwin Randolf Cole.  The removal of unknown image blurs by homomorphic filtering , 1973 .

[17]  B. R. Hunt,et al.  The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer , 1973, IEEE Transactions on Computers.

[18]  N. Nahi,et al.  Recursive Image Enhancement - Vector Processing , 1973, IEEE Transactions on Communications.

[19]  Harry C. Andrews.  Digital image restoration: A survey , 1974, Computer.

[20]  Arun N. Netravali,et al.  Image Restoration Based on a Subjective Criterion , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  M. Srinath,et al.  Interpolative models in restoration and enhancement of noisy images , 1977 .

[22]  Y Ichioka,et al.  Image restoration by Wiener filtering in the presence of signal-dependent noise. , 1977, Applied optics.

[23]  JOHN w. WOODS,et al.  Kalman filtering in two dimensions , 1977, IEEE Trans. Inf. Theory.

[24]  Bobby R. Hunt,et al.  Bayesian Methods in Nonlinear Digital Image Restoration , 1977, IEEE Transactions on Computers.

[25]  L. Silverman,et al.  Digital restoration of images degraded by general motion blurs , 1977 .

[26]  B. Prasada,et al.  Adaptive quantization of picture signals using spatial masking , 1977, Proceedings of the IEEE.

[27]  Anil K. Jain,et al.  A Semicausal Model for Recursive Filtering of Two-Dimensional Images , 1977, IEEE Transactions on Computers.

[28]  Michael G. Strintzis,et al.  Dynamic representation and recursive estimation of cyclic and two-dimensional processes , 1978 .

[29]  C. Rubinstein,et al.  On the Design of Quantizers for DPCM Coders: Influence of the Subjective Testing Methodology , 1978, IEEE Trans. Commun..

[30]  C. Rubinstein,et al.  On the Design of Quantizers for DPCM Coders: A Functional Relationship Between Visibility, Probability and Masking , 1978, IEEE Trans. Commun..

[31]  Sheldon S. L. Chang.  Digital linear processor theory and optimum multidimensional data estimation , 1979 .