Reconstruction is imperative whenever an image needs to be resampled as a result of transformation such as an affine or perspective transform, or texture mapping. We present a new method for the characterization and measurement of reconstruction error. Our method, based on spatial domain error analysis, uses approximation theory to develop error bounds. We provide, for the first time, an effici...

Approximate message passing (AMP) is a class of low-complexity scalable algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal β0 from noisy, linear measurements y = Aβ0 + w. AMP has the attractive feature that its performance (for example, the mean squared error of its estimates) can be accurately tracked by a simple, scalar iteration refe...

The reconstruction of an image from incomplete view data requires the use of several constraints not derived from ray sum (projection data) measurements. The constraints can be incorporated through the method of (sequential and parallel) projections onto the constraint sets. These methods for the use of information regarding the noise and the image are implemented and compared in this paper. I ...

Slicing operation is a most powerful and useful tool for the exploration of volume data. In the core of the slicing algorithm is a resampling process that produces a set of new samples constituting the new slice. Reconstruction is imperative whenever an image or a volume needs to be resampled as a result of an affine or perspective transformation, texture mapping, or volume slicing. Traditional...

Since the landmark paper in 1992 by A. Jacquin [1] on image coding with iterated function systems (IFS), many authors have studied IFS (or "fractal") and proposed many improvements to Jacquin’s algorithm [2]. While IFS has been viewed as a promising technique that might overtake more established coding methods, generally it has not so far lived up to these expectations. One fundamental problem ...

In this paper, we propose a method to estimate the initial state of linear dynamical system from noisy observation based on Kalman Filters and Optimal Smoothing techniques. The allows user have estimations in real-time, that is, new estimation for each observation. Moreover, at step, covariance matrix error is found, one minimizes variance after applying filter. We analyze stability when there ...