Iterative Restoration Algorithm Research Articles

A class of iterative signal restoration algorithms

A class of iterative signal restoration algorithms is derived based on a representation theorem for the generalized inverse of a matrix. These algorithms exhibit a first or higher order of convergence, and some of them consist of an online and an offline computational part. The conditions for convergence, the rate of convergence of these algorithms, and the computational load required to achieve the same restoration results are derived. An iterative algorithm is also presented which exhibits a higher rate of convergence than the standard quadratic algorithm with no extra computational load. These algorithms can be applied to the restoration of signals of any dimensionality. The presented approach unifies a large number of iterative restoration algorithms. Based on the convergence properties of these algorithms, combined algorithms are proposed that incorporate a priori knowledge about the solution in the form of constraints and converge faster than previously published algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Iterative methods for image deblurring

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.

New termination rule for linear iterative image restoration algorithms

Every iterative restoration algorithm requires some performance measure to determine the termination point for the iteration. Typically, the termination rule is based on a measure of the residual or the change in the solution from one iteration to the next. A better rule would be one that terminates the iteration when the distance between the original undistorted image and restored image is minimized in some sense. In this paper, we present a performance measure that estimates this distance without prior knowledge of the original image. Our measure relies on evaluating a spectral filter function at each step of the iteration. These functions describe the solution at each step in terms of the singular value decomposition of the system matrix. As such, spectral filter functions provide valuable insight into the behavior of an iteration as well as a means of defining a termination rule. We develop a general technique for determining the spectral filter functions for a given iteration, which we demonstrate by applying it to a linear iterative image restoration algorithm.

Adaptive iterative image restoration with reduced computational load

In this paper, methods for reducing the computational load of an adaptive iterative image restoration algorithm while producing a restored image of high visual quality are proposed. These methods are based on a class of iterative restoration algorithms that exhibit a first- or higher-order convergence, and some of them consist of on-line and off-line computational parts. Since only the first-order or linear algorithm can take a computationally feasible adaptive formulation for image restoration, iterative algorithms that combine the linear and higher-order algorithms are proposed. These algorithms converge to the weighted minimum norm least-squares solution with significantly less computational load cornpared to the adaptive linear algorithm. The quality of the adaptively restored image depends on the choice of the weight coefficients, which are evaluated based on the spatial activity of the image. Various methods for computing the local spatial activity in the image are proposed. These methods are shown to produce visually better restoration results. Also, a method for computing the weight coefficients only at the edges is proposed, which results in additional computational savings. Finally, experimental results are presented and the various restoration methods are compared with respect to their computational complexity, the mean squared error, and the visual quality of the restored images.

Iterative Image Restoration Algorithms

This tutorial paper discusses the use of successive-approximation-based iterative restoration algorithms for the removal of linear blurs and noise from images. Iterative algorithms are particularly attractive for this application because they allow for the incorporation of prior knowledge about the class of feasible solutions, because they can be used to remove nonstationary blurs, and because they are fairly robust with respect to errors in the approximation of the blurring operator. Regularization is introduced as a means for preventing the excessive noise magnification that is typically associated with ill-posed inverse problems such as the deblurring problem. Iterative algorithms with higher convergence rates and a multistep iterative algorithm are also discussed. A number of examples are presented.

Single and multistep iterative image restoration and VLSI implementation

A synchronous VLSI implementation of an iterative image restoration algorithm is described in this paper. This implementation is based on a single-step, as well as on a multistep iterative algorithm derived from the single-step regularized iterative restoration algorithm. One processor is assigned to each picture element, with local memory depending on the support of the restoration filter. The implementation, which consists of interprocessor communication and intraprocessor computations, is provided and convergence issues are discussed.

Digital Restoration of Scintigraphic Images by a Two-Step Procedure

A two-step procedure for restoring scintigraphic images is described. The first step uses a local-statistics algorithm for improvement in signal-to-noise ratio by smoothing the Poisson noise. The second step aims at improvement in spatial resolution by removing the linear blur using the iterative restoration algorithm. We present some results of computer simulations and restoration of scintigraphic images that demonstrate the effectiveness of the proposed procedure.

General iterative method of restoring linearly degraded images

A generalized iterative restoration algorithm for linearly degraded images is presented, based on the singular value decomposition of the degradation operator. Covergence of the algorithm is accelerated by imposing constraints on the solution. Realizations of the restoration algorithm for various types of degradation are presented, and the analogy to a modified version of the method by Gerchberg [ Opt. Acta21, 709 ( 1974)] and Papoulis [ IEEE Trans. Circuits Syst.CAS-22, 735 ( 1975)] is discussed. Results from computer-simulated images are given, and the effects of noise on the restored images are considered. The performance of the algorithm is found to be superior to that of pseudoinverse techniques.

Enhancement of event related potentials by iterative restoration algorithms.

An iterative procedure for the restoration of event related potentials (ERP) is proposed and implemented. The method makes use of assumed or measured statistical information about latency variations in the individual ERP components. The signal model used for the restoration algorithm consists of a time-varying linear distortion and a positivity/negativity constraint. Additional preprocessing in the form of low-pass filtering is needed in order to mitigate the effects of additive noise. Numerical results obtained with real data show clearly the presence of enhanced and regenerated components in the restored ERP's. The procedure is easy to implement which makes it convenient when compared to other proposed techniques for the restoration of ERP signals.

An iterative restoration technique

An iterative restoration algorithm for the solution of x in y = Hx has been described. For the purpose of comparison, a general overview of the existing iterative techniques is given. For the proposed technique, the constraints for convergence and its rate, which is quadratic in comparison with the linear rate of other techniques, have been derived. Also derived is the deviation in the solution when instead of H a perturbed operator H ∗ is used in the algorithm. The effect of additive noise on the estimates has also been described. Finally, the technique has been applied to the deconvolution of a blurred signal, the results of which validate the theory. For the sake of comparison, the algorithm has been applied to the sample of Fig. 7 of Schafer, Mersereau and Richards (1981). It is seen that only four iterations compared with twenty in the cited reference are sufficient to produce similar results.

Error analysis of a class of constrained iterative restoration algorithms

In this paper, we investigate the problem of noise stability in a class of iterative image restoration algorithms. The algorithm is a Gerchberg-Papoulis type algorithm that utilizes incomplete information and partial constraints to specify constraint operators for the iteration. The iteration, in the absence of noise, converges to a unique solution. In the presence of noise, the restoration is considered as an ill-posed problem. In this study, noise stability of the algorithm is investigated. A general error-analysis method is derived to predict the optimum number of iterations that minimizes the mean-square error between the ideal and the restored image. The tradeoff between signal reconstruction and noise amplification has been investigated, and it has been shown that by using prior knowledge of the signal and noise statistics, it is possible to achieve optimal restoration. Simulations have been performed to verify the theoretical results.

A method of iterative data refinement and its applications

AbstractIterative data refinement (IDR) is a general procedure for producing a sequence of estimates of the data that would be collected by a measuring device which is idealized to a certain extent, starting from the data that are collected by an actual measuring device. Following a discussion of the fundamentals of IDR, we present a number of previously published procedures which are special cases of it. We concentrate on examples from medical imaging. In particular, we discuss beam hardening correction in x‐ray computerized tomography, attenuation correction in emission computerized tomography, and compensation for missing data in reconstruction from projections. We also show that a standard method of numerical mathematics (the parallel chord method) as well as a whole family of constrained iterative restoration algorithms are special cases of IDR. Thus IDR provides a common framework within which a number of originally different looking procedures are presented and discussed. We also present a result of theoretical nature concerning the initial behavior of IDR.

Signal restoration from phase by projections onto convex sets

We apply the method of alternating projections onto convex sets to the problem of restoring a signal from the phase of its Fourier transform. A method of improving convergence by adaptively varying a set of relaxation parameters in the restoration algorithm is described. The advantages of using the method of convex projections over other iterative restoration algorithms are discussed and illustrated.

Closed-form object restoration from limited spatial and spectral information

Given only a portion of an arbitrary finite-energy [L(2) (-infinity, infinity)] image and a portion of that image's spectrum, we present a closed-form method by which the entire image can be reconstructed. The algorithm is a basic augmentation of a recently proposed iterative restoration algorithm presented by Stark et al. [J. Opt. Soc. Am. 71, 635 (1981); Opt. Lett. 6, 259 (1981)]. Experimental results are presented.

Constrained iterative restoration algorithms

This paper describes a rather broad class of iterative signal restoration techniques which can be applied to remove the effects of many different types of distortions. These techniques also allow for the incorporation of prior knowledge of the signal in terms of the specification of a constraint operator. Conditions for convergence of the iteration under various combinations of distortions and constraints are explored. Particular attention is given to the use of iterative restoration techniques for constrained deconvolution, when the distortion band-limits the signal and spectral extrapolation must be performed. It is shown that by predistorting the signal (and later removing this predistortion) it is possible to achieve spectral extrapolation, to broaden the class of signals for which these algorithms achieve convergence, and to improve their performance in the presence of broad-band noise.