A Semicausal Model for Recursive Filtering of Two-Dimensional Images

A two-dimensional discrete stochastic model for representing images is developed. This representation has lower mean square error, compared to a standard autoregressive Markov representation. Application of the model to linear filtering of images degraded by white noise leads to scalar recursive filtering equations requiring only 0(N2log2N) computations for N x N images. The filter algorithm is a hybrid algorithm where the image is transformed along one dimension and spatially filtered, recursively, in the other. Examples on a 255 X 255 image are given.

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

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

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

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

[5]  M. P. Ekstrom,et al.  OPTIMUM DESIGN OF TWO-DIMENSIONAL NONRECURSIVE DIGITAL FILTERS. , 1970 .

[6]  G. Robbins,et al.  Image restoration for a class of linear spatially-variant degradations , 1970, Pattern Recognit..

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

[8]  Edward Angel,et al.  Cauchy Problems for Ordinary Differential, Difference and Integral Equations , 1971 .

[9]  Ronald S. Hershel.  UNIFIED APPROACH TO RESTORING DEGRADED IMAGES IN THE PRESENCE OF NOISE , 1971 .

[10]  Thomas S. Huang,et al.  Inverse filtering for linear shift-variant imaging systems , 1972 .

[11]  William K. Pratt,et al.  Generalized Wiener Filtering Computation Techniques , 1972, IEEE Transactions on Computers.

[12]  A. Habibi.  Two-dimensional Bayesian estimate of images , 1972 .

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

[14]  A. Sawchuk.  Space-variant image motion degradation and restoration , 1972 .

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

[16]  M. M. Sondhi,et al.  Image restoration: The removal of spatially invariant degradations , 1972 .

[17]  Ernest L. Hall.  A comparison of computations for spatial frequency filtering , 1972 .

[18]  Anil K. Jain,et al.  A dimensionality reducing model for distributed filtering , 1973 .

[19]  Leonard M. Silverman,et al.  State space image motion restoration , 1973, CDC 1973.

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

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

[22]  Anil K. Jain,et al.  Image Restoration, Modelling, and Reduction of Dimensionality , 1974, IEEE Transactions on Computers.

[23]  A. Jain,et al.  A Fast Karhunen-Loeve Transform for a Class of Random Processes , 1976, IEEE Trans. Commun..

[24]  M. Strintzis,et al.  Comments on "Two dimensional Bayesian estimate of images" , 1976 .

[25]  A. K. Jain.  Computer program for fast Karhunen Loeve transform algorithm , 1976 .

[26]  Anil K. Jain.  A Fast Karhunen-Loeve Transform for Digital Restoration of Images Degraded by White and Colored Noise , 1977, IEEE Transactions on Computers.