Developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined. Particular attention is paid to common estimation structures and to practical problems not properly solved yet. The problem of image reconstruction and restoration is first formulated. Some of the current regularization approaches used to solve the problem are then described. The concepts of a priori information and compound criterion are introduced. A Bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated. The practical aspects of computing the solution, first when the hyperparameters are known and second when they must be estimated, are then considered. Conclusions are drawn, and points that still need to be investigated are outlined. >

Image reconstruction and restoration: overview of common estimation structures and problems

The authors discuss the use of iterative restoration algorithms for the removal of linear blurs from photographic images that may also be assumed to be degraded by pointwise nonlinearities such as film saturation and additive noise. Iterative algorithms allow for the incorporation of various types of prior knowledge about the class of feasible solutions, can be used to remove nonstationary blurs, and are fairly robust with respect to errors in the approximation of the blurring operator. Special attention is given to the problem of convergence of the algorithms, and classical solutions such as inverse filters, Wiener filters, and constrained least-squares filters are shown to be limiting solutions of variations of the iterations. Regularization is introduced as a means for preventing the excessive noise magnification that is typically associated with ill-conditioned inverse problems such as the deblurring problem, and it is shown that noise effects can be minimized by terminating the algorithms after a finite number of iterations. The role and choice of constraints on the class of feasible solutions are also discussed. >

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Iterative methods for image deblurring

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. A neural network model is used to represent a possibly nonstationary image whose gray level function is the simple sum of the neuron state variables. The restoration procedure consists of two stages: estimation of the parameters of the neural network model and reconstruction of images. Owing to the model's fault-tolerant nature and computation capability, a high-quality image is obtained using this approach. A practical algorithm with reduced computational complexity is also presented. A procedure for learning the blur parameters from prototypes of original and degraded images is outlined. >

Image restoration using a neural network

We present a tutorial review of recent developments in restoring images that are degraded by both blur and noise. We consider three fundamental aspects of digital image restoration: modeling, identification
algorithms, and restoration algorithms. An overview of modeling the degradations, and certain properties of images are given first. We then survey the methods that identify these models. Image restoration algorithms are surveyed in two categories: general algorithms and specialized algorithms. We briefly discuss present and future research topics in the field. Our emphasis here is on fundamental concepts and ideas rather than mathematical details.

Survey of recent developments in digital image restoration.

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; an area image sensor for sensing an image and generating pixel data representing the image; a linear image sensor for scanning the array of dots on the card and converting the array of dots into a data signal; a microcontroller provided in the housing, the microcontroller for decoding the data signal into the programming script and applying the programming script on the pixel data; and a printing mechanism for printing the pixel data, having applied thereto the programming script, on the roll of print media. The microcontroller integrates on a single chip a VLIW processor, a printhead interface, and an output buffer effecting communication between the VLIW processor and the printhead interface.

Image sensing and printing device

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.

J. Rieske

Papers

A fast Kalman filter for images degraded by both blur and noise