Iterative Signal Restoration Research Articles

Iterative signal restoration by sine transform based preconditioners

A novel sine transform based preconditioned conjugate gradient (PCG) method for signal restoration is presented. If the bandwidth 2? +1 in the model matrix is a constant, then the asymptotic complexity for the new algorithm is O(N) per iterative step, where Nis the order of the model. This complexity is reduced by an order of magnitude in comparison with the known fast Fourier transform (FFT) technique proposed recently in the literature. Moreover, if ? has a size similar to N, then the new PCG method is accomplished by the fast sine transform (FST) and the fast Hartley transform (FHT). The computational and storage cost per preconditioning step for the new PCG method is reduced by 50% as compared to the FFT approach. To stabilize the computation, a special Tikhonov regularization is introduced. Numerical experimentations show that the new PCG method is of a speedy convergence rate. The new PCG methods maintain less computational complexity per iterative step and have a better convergence rate than the other known PCG methods.

Another stopping rule for linear iterative signal restoration

A new stopping rule is proposed for linear, iterative signal restoration using the gradient descent and conjugate gradient algorithms. The stopping rule attempts to minimize MSE under the assumption that the signal arises from a white noise process. This assumption is appropriate for many coherent imaging applications. The stopping rule is trivial to compute and, for fixed relaxation parameters, can be computed prior to starting the iteration. The utility of the stopping rule is demonstrated through the restoration of MR imagery.

A practical stopping rule for iterative signal restoration

Iterative signal restoration is a common and simple approach for recovering degraded signals. Unfortunately, iterative algorithms often converge slowly, and the convergence point is usually not the best restoration because of noise amplification. Therefore, a stopping rule should be imposed to maximize the effectiveness of the iterative algorithm. We demonstrate the value of randomized generalized cross-validation (RGCV) as a stopping rule for linear iterative restoration algorithms with simple initial conditions and show that it can be used on relatively small data sets with confidence. We also illustrate the performance of the RGCV criterion for various degrees of blurring and noise. >

A new iterative signal restoration method

A new iterative method for signal restoration has been presented. An estimate operatorW k which is related to error operatorB k in the restoration process is introduced to decrease the estimate error and increase the convergence rate. The effect of noise on the estimate process has also been described. Finally, the method has been applied to the deconvolution of a blurred signal, and the results validate the method. A comparison between the presented method and the general method has also been given.

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>

Convergence criteria for iterative restoration methods

While many iterative signal restoration methods have been shown to converge in the mathematical sense, a practical criterion is needed to indicate when the numerical algorithm has converged. The use of the residual signal in defining such a criterion is investigated. The advantage of this criterion over the criterion of examining successive iterations is demonstrated.

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.