Survey of estimation techniques in image restoration

Blurred and noisy images can often be represented as nonstationary 2D stochastic processes that can be modeled by a set of linear space-varying state equations, or by an ARMA input-output equation with space-varying coefficients. Liner difference equation models for characterizing both images and their degraded observations are reviewed. The models are then expressed in state-space form suitable for Kalman filtering and in input-output equation form suitable for maximum likelihood parameter identification and ARMA smoothing. Recent methods for blur identification, image parameter identification, and simultaneous image and blur identification are reviewed. The fundamentals of image restoration are briefly summarized, and three approaches are discussed: iterative deterministic regularized restoration, restoration using optimal filtering, and adaptive restoration. Some representative results are given, and recommendations for future research topics are made.<<ETX>>

[1]  Reginald L. Lagendijk,et al.  Identification and restoration of noisy blurred images using the expectation-maximization algorithm , 1990, IEEE Trans. Acoust. Speech Signal Process..

[2]  A. T. Erdem,et al.  Decision-directed adaptive image restoration using multiple image and blur models , 1989, Proceedings. ICCON IEEE International Conference on Control and Applications.

[3]  J. J. Gerbrands,et al.  A fast Kalman filter for images degraded by both blur and noise , 1983 .

[4]  A. Murat Tekalp,et al.  Edge-adaptive Kalman filtering for image restoration with ringing suppression , 1989, IEEE Trans. Acoust. Speech Signal Process..

[5]  Reginald L. Lagendijk,et al.  Regularized iterative image restoration with ringing reduction , 1988, IEEE Trans. Acoust. Speech Signal Process..

[6]  J. Woods,et al.  Identification and restoration of images with symmetric noncausal blurs , 1988 .

[7]  J. Woods,et al.  Estimation and identification of two dimensional images , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[8]  H. Trussell,et al.  The feasible solution in signal restoration , 1984 .

[9]  B. R. Hunt,et al.  Digital Image Restoration , 1977 .

[10]  L. Silverman,et al.  Image model representation and line-by-line recursive restoration , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[11]  L. Silverman,et al.  Restoration of motion degraded images , 1975 .

[12]  Jan J. Gerbrands,et al.  An Edge-Preserving Recursive Noise-Smoothing Algorithm for Image Data , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  Zhe Wu,et al.  Multidimensional state-space model Kalman filtering with application to image restoration , 1985, IEEE Trans. Acoust. Speech Signal Process..

[14]  P. Wellstead,et al.  Input/output self-tuning algorithms applied to image processing , 1987, 26th IEEE Conference on Decision and Control.

[15]  A. Murat Tekalp,et al.  Maximum likelihood image and blur identification: a unifying , 1990 .

[16]  N. Nahi Role of recursive estimation in statistical image enhancement , 1972 .

[17]  J. Woods,et al.  Kalman filtering in two dimensions: Further results , 1981 .

[18]  Tohru Katayama Restoration of Noisy Images Using a Two-Dimensional Linear Model , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  J. Woods,et al.  Model-based segmentation and space-variant restoration of blurred images by decision-directed filtering , 1988 .

[20]  H. Kaufman,et al.  Image restoration using reduced order models , 1988 .

[21]  S. Rajala,et al.  Adaptive nonlinear image restoration by a modified Kalman filtering approach , 1981 .

[22]  John W. Woods,et al.  Multiple model recursive estimation of images , 1979, ICASSP.

[23]  A. Murat Tekalp,et al.  Quantitative analysis of artifacts in linear space-invariant image restoration , 1990, Multidimens. Syst. Signal Process..

[24]  A. Murat Tekalp,et al.  Identification of image and blur parameters for the restoration of noncausal blurs , 1986, IEEE Trans. Acoust. Speech Signal Process..

[25]  G. Pavlovic,et al.  Restoration in the presence of multiplicative noise with application to scanned photographic images , 1990, International Conference on Acoustics, Speech, and Signal Processing.

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

[27]  Hsien-Che Lee Review of image-blur models in a photographic system using the principles of optics , 1990 .

[28]  Peter Wellstead,et al.  Self-tuning filters and predictors for two-dimensional systems Part 1: Algorithms , 1985 .

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

[30]  Tohru Katayama,et al.  Restoration of images degraded by motion blur and noise , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[31]  Mandyam D. Srinath,et al.  Sequential Estimation Technique for Enhancement of Noisy Images , 1977, IEEE Transactions on Computers.

[32]  A. Murat Tekalp,et al.  Fast recursive estimation of the parameters of a space-varying autoregressive image model , 1985, IEEE Trans. Acoust. Speech Signal Process..

[33]  T.F. Quatieri,et al.  Statistical model-based algorithms for image analysis , 1986, Proceedings of the IEEE.

[34]  N. Nahi,et al.  Decision-directed recursive image enhancement , 1975 .

[35]  R.W. Schafer,et al.  Constrained iterative restoration algorithms , 1981, Proceedings of the IEEE.

[36]  B. Suresh,et al.  New results in two-dimensional Kalman filtering with applications to image restoration , 1981 .