V. Z. Mesarovi c, N. P. Galatsanos, and A. K. Katsaggelos, "Regularized constrained total least squares image restoration," IEEE Trans. Image Processing, vol. 4, pp. 1096--1107, Aug. 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....constraint that the norm of the solution vector x is speci ed. Note that this problem was posed in Pruessner and O Leary [7] This corresponds to a Tikhonov regularization of our structured total least squares problem and results in a fast solution algorithm for the problem considered in [5, 6, 7]. The core of the algorithm in [4] based on a more general algorithm of [8] relies on two results: the representation of the generators for the matrix M M that appears in the normal equations when A is Toeplitz, and then a fast factorization of a matrix derived from these generators. So we ....

V. Mesarovi c, N. Galatsanos, and A. Katsaggelos, Regularized constrained total least squares image restoration, IEEE Transactions on Image Processing, 4 (1995), pp. 1096{ 1108.

....obtain useful results. In this paper it is shown how to implement Tikhonov regularization [20, 24] to arrive at the regularized structured total least norm (RSTLN) algorithm. While implementations of Tikhonov regularization for constrained total least squares problems had been developed previously [15, 17], the rst even before the work of Rosen et al. on the simpler problem, they focused solely on the 2 norm case. The contributions herein are the extension for p = 1 and p = 1 norms and the comparison of methods. In the p = 1 and p = 1 cases, the main computational task lies in solving a linear ....

V. Mesarovi c, N. Galatsanos, and A. Katsaggelos, Regularized constrained total least squares image restoration, IEEE Transactions on Image Processing, 4, (1995), pp. 1096{ 1108.

....the set of equations in (1) where both H and g are contaminated with noise [1] 3] For shift invariant blurs, the special structure of H and 1H can be exploited in the constrained TLS (CTLS) technique [4] to obtain better estimates. Recently, a regularized version of CTLS was demonstrated in [5], which attempts to preserve smoothness properties of the signal through the introduction of a regularization operator. While these estimation schemes are statistically sound, they do not permit use of other a priori knowledge of the signal in the estimation procedure. Set theoretic estimation ....

V. Z. Mesarovi c, N. P. Galatsanos, and A. K. Katsaggelos, "Regularized constrained total least squares image restoration," IEEE Trans. Image Processing, vol. 4, pp. 1096--1107, Aug. 1995.

....A T b ; where D ff is a diagonal matrix of the form D ff = diagfff 1 I ; ff 2 I ; ff K Ig ; and the fff i g are certain nonnegative scalar regularization parameters. Such regularized solutions have been used extensively in signal and image processing applications (see, e.g. 11] [14]) and in adaptive filtering (see, e.g. 15] 16] 4. A major issue in applications (see, e.g. the titles of [12] 14] is always how to select the regularization parameters. It turns out that the BDU solution leads to an automatic selection of the parameters fff i g. More explicitly, these ....

....are certain nonnegative scalar regularization parameters. Such regularized solutions have been used extensively in signal and image processing applications (see, e.g. 11] 14] and in adaptive filtering (see, e.g. 15] 16] 4. A major issue in applications (see, e.g. the titles of [12] [14]) is always how to select the regularization parameters. It turns out that the BDU solution leads to an automatic selection of the parameters fff i g. More explicitly, these parameters will be shown to be the unique nonnegative roots of certain coupled equations that are fully determined from the ....

V. Z. Mesarovi'c, N. P. Galatsanos, and A. K. Katsaggelos, Regularized constrained total least squares image restoration, IEEE Transactions on Image Processing, vol. 4, no. 8, pp. 1096--1108, August 1995.

....and 2.2(d) are similar, yet Fig. 2.2(e) shows that the least squares solution fails in the perturbed case. Several regularization methods that are superior to the pure least squares method have been proposed in the literature for image restoration purposes, some of which are discussed in [24] [28]. We shall have more to say about regularization in the sequel (see Secs. 3.1 and 5.6) 2.4. Linear Quadratic Regulator Example. Another well known manifestation of the sensitivity of least squares based designs to modeling errors occurs in quadratic control (see, e.g. 9, 11, 30, 33] In the ....

.... due to the fact that the coefficient matrix (A T A flI) is always invertible (in fact, positive definite and better conditioned than A T A in the pure least squares method) Applications of such regularized costs in the image processing context abound and can be found, for example, in [24] [28]. It will turn out that the BDU methods discussed further ahead in this paper perform automatic regularization. That is, while the above classical regularization method still requires an intelligent selection of the parameter fl by the designer, the BDU methods will select the the parameter fl ....

V.Z. Mesarovi'c and N.P. Galatsanos and A.K. Katsaggelos, Regularized constrained total least squares image restoration, IEEE Transactions on Image Processing, vol. 4, no. 8, pp. 1096--1108, August 1995.

....algorithm design and system level problems that cause the ill posed nature of the object image formation and restoration tasks. The problem of image formation and restoration has been extensively investigated in the literature by the use of both continuous variables functional and digital methods [1 5], etc. In the multi sensor industrial vision (IV) and remote sensing (RS) the measured field produced by all radiating scattering sources distributed over the extended object is usually converted to the digital data recordings available for further processing. In the literature, a majority of ....

....etc. To develop the technique that generates high resolution accurate images for environmental monitoring scenarios with an arbitrary sensor arrays and unknown statistics of the signals and medium, we relax here the conventional assumptions of standard Bayesian inference to the IV RS problems [3, 5]. We propose to fuse the experiment design considerations and robust regularization methods for reconstructing the object image degraded by a stochastic SFO and additive noise from the finite set of digital data recordings. The proposed approach employs the model based control of the experiment ....

[Article contains additional citation context not shown here]

A. Mesarovic, N.P. Galatsanos, and A.K. Katsaggelos, "Regularized Constrained Total Least Squares Image Restoration", IEEE Trans. Image Proc., vol. 4, pp. 1096-1108, 1995.

....matrix occasionally measured, or more commonly simply computed based on an approximate geometry. In either case A contains errors, and the effect of this model mismatch on is poorly understood. The errors in A might invite the application of the total least squares (TLS) estimation method, e.g. [43]. However, TLS essentially assumes that the errors in A are normally distributed, which is very questionable in PET. Furthermore, A usually includes attenuation factors that are determined from separate noisy transmission scans. Understanding the effects of both deterministic and random errors in ....

V Z Mesarovi'c, N P Galatsanos, and A K Katsaggelos. Regularized constrained total least squares image restoration. IEEE Tr. Im. Proc., 4(8):1096--1109, August 1995.

....and the accuracy of the support constraints for this class of methods [15] A statistical technique for situations in which an inaccurate noisy PSF estimate is available has been developed. In this method image restoration is performed using a regularized constrained total least squares approach [16]. ....

V. Z. Mesarovi'c, N. P. Galatsanos And A. K. Katsaggelos, "Regularized constrained total least squares image restoration," IEEE Trans. Image Processing, vol. 4(8), pp. 1096--1108, Aug. 1995.

....that controls the tradeoff between resolution and noise was not estimated systematically. In [2] and [22] the problem under consideration was addressed using the theory of projections onto convex sets. However, these convex sets were described by parameters which were assumed known a priori. In [15] this problem was addressed using the regularized constrained total least squares (RCTLS) framework. However, the parameters that define the RCLTS filter were again assumed known a priori. In the classical restoration problem, where the PSF is exactly known, the ratio of the observation noise ....

....white noise with covariance matrix , where denotes the variance of the observation noise. Furthermore, the noises in the observed data and the PSF are assumed independent of each other and independent from the source image . In this case, the image degradation can be described by the model [7] [15], 24] 25] 4) in which (5) and are lexicographically ordered representations of the observed degraded image, the source image, and the additive noise in the observed image, respectively. The matrix is the known (assumed, estimated or measured) component of the PSF matrix is the unknown ....

[Article contains additional citation context not shown here]

V. Z. Mesarovic , N. P. Galatsanos, and A. K. Katsaggelos, "Regularized constrained total least-squares image restoration," IEEE Trans. Image Processing, vol. 4, pp. 1096--1108, Aug. 1995.

No context found.

V. Z. Mesarovi'c, N. P. Galatsanos and A. K. Katsaggelos, "Regularized Constrained Total Least-Squares Image Restoration", SPIE-Proceedings of VCIP-94, Vol. 2, pp. 1301-1312, Chicago, September 1994.

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V. Z. Mesarovi'c, N. P. Galatsanos and A. K. Katsaggelos, "Regularized Constrained Total Least-Squares Image Restoration", IEEE Trans. Image Processing, Vol.4, No. 8, pp. 1096-1108, August 1995.

No context found.

V. Z. Mesarovi c, N. P. Galatsanos, and A. K. Katsaggelos, "Regularized constrained total least squares image restoration," IEEE Trans. Image Processing, vol. 4, pp. 1096--1107, Aug. 1995.

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