Proceedings ArticleDOI
A fast Kalman filter for images degraded by both blur and noise
Jan Biemond
- Vol. 7, pp 1146-1149
Reads0
Chats0
TLDR
An optimal line-by-line recursive Kalman filter is derived for restoring images which are degraded in a deterministic way by linear blur and in a stochastic way by additive white noise.Abstract:
An optimal line-by-line recursive Kalman filter is derived for restoring images which are degraded in a deterministic way by linear blur and in a stochastic way by additive white noise. To reduce the computational and storage burden imposed by this line-by-line recursive Kalman filter circulant matrix approximations are made in order to diagonalize - by means of the fast Fourier transform (FFT) - both the model matrices and the distortion matrix in the dynamical model of the total image-recording system. Then the dynamical model reduces to a set of N decoupled equations and the line-by-line recursive Kalman filter based on this model reduces to a set of N scalar Kalman filters suitable for parallel processing of the data in the Fourier domain. Finally, via an inverse FFT the filtered data is presented in the data domain. The total number of computations for an N×N image reduces from the order of 0(N4) to 0(N^{2}\log_{2}N) .read more
Citations
More filters
Journal ArticleDOI
Image reconstruction and restoration: overview of common estimation structures and problems
TL;DR: The problem of image reconstruction and restoration is first formulated, and some of the current regularization approaches used to solve the problem are described, and a Bayesian interpretation of the regularization techniques is given.
Journal ArticleDOI
A fast Kalman filter for images degraded by both blur and noise
TL;DR: A fast Kalman filter is derived for the nearly optimal recursive restoration of images degraded in a deterministic way by blur and in a stochastic way by additive white noise.
Journal ArticleDOI
Identification and restoration of images with symmetric noncausal blurs
TL;DR: In this article, a parallel identification and restoration procedure for images with symmetric, noncausal blurs is described, where the identification problem can be specified as a parallel set of one-dimensional complex autoregressive moving-average (ARMA) identification problems.
Journal ArticleDOI
Weight assignment for adaptive image restoration by neural networks
Stuart William Perry,L. Guan +1 more
TL;DR: It is shown that the previously proposed neural-network method based on gradient descent can only find suboptimal solutions, and then a regional processing approach based on local statistics is introduced.
Proceedings ArticleDOI
Boundary value problem in image restoration
TL;DR: The purpose of this paper is to demonstrate the importance of the boundary values in image restoration and to show how to improve the transient response of the steady-state Kalman filters in [2] and [3] with better choices for the boundaryvalues.
References
More filters
Journal ArticleDOI
On the asymptotic eigenvalue distribution of Toeplitz matrices
TL;DR: This tutorial paper proves the Szegio theorem for the special case of finite-order Toeplitz matrices, which is both simple and intuitive and contains the important concepts involved in the most general case.
Journal ArticleDOI
Advances in mathematical models for image processing
TL;DR: Several state-of-the-art mathematical models useful in image processing are considered, including the traditional fast unitary transforms, autoregessive and state variable models as well as two-dimensional linear prediction models.
Journal ArticleDOI
A Sinusoidal Family of Unitary Transforms
TL;DR: A new family of unitary transforms is introduced and it is shown that the well-known discrete Fourier, cosine, sine, and the Karhunen-Loeve (KL) (for first-order stationary Markov processes) transforms are members of this family.
Journal ArticleDOI
A survey of sparse matrix research
TL;DR: This paper surveys the state of the art in sparse matrix research in January 1976, and discusses the solution of sparse simultaneous linear equations, including the storage of such matrices and the effect of paging on sparse matrix algorithms.
Journal ArticleDOI
Kalman filtering in two dimensions: Further results
John W. Woods,V. Ingle +1 more
TL;DR: The two-dimensional reduced update Kalman filter is extended to the deconvolution problem of image restoration and a more thorough treatment of the uniquely two- dimensional boundary condition problems is provided.