Journal ArticleDOI
A fast Kalman filter for images degraded by both blur and noise
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TLDR
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.Abstract:
In this paper 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. Straightforwardly implemented optimal restoration schemes for two-dimensional images degraded by both blur and noise create dimensionality problems which, in turn, lead to large storage and computational requirements. When the band-Toeplitz structure of the model matrices and of the distortion matrices in the matrix-vector formulations of the original image and of the noisy blurred observation are approximated by circulant matrices, these matrices can be diagonalized by means of the FFT. Consequently, a parallel set of N dynamical models suitable for the derivation of N low-order vector Kalman filters in the transform domain is obtained. In this way, the number of computations is reduced from the order of O(N4) to that of O(N^{2} \log_{2} N) for N × N images.read more
Citations
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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
Iterative methods for image deblurring
TL;DR: In this paper, the authors discuss the use of iterative restoration algorithms for the removal of linear blurs from photographic images that may also be degraded by pointwise nonlinearities such as film saturation and additive noise.
Journal ArticleDOI
Image restoration using a neural network
TL;DR: An approach for restoration of gray level images degraded by a known shift invariant blur function and additive noise is presented using a neural computational network and a high-quality image is obtained using this approach.
Journal ArticleDOI
Survey of recent developments in digital image restoration.
M. Ibrahim Sezan,A. Murat Tekalp +1 more
TL;DR: A tutorial review of recent developments in restoring images that are degraded by both blur and noise and considers three fundamental aspects of digital image restoration: modeling, identification algorithms, and restoration algorithms.
Patent
Image sensing and printing device
TL;DR: In this article, an image sensing and printing digital camera device includes a housing defining a slot for receiving a printed instruction card having printed thereon an array of dots representing a programming script, the housing further storing therein a roll of print media.
References
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TL;DR: Parts of image processing are discussed--specifically: the mathematical operations one is likely to encounter, and ways of implementing them by optics and on digital computers; image description; and image quality evaluation.
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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.
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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.
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A survey of sparse matrix research
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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.