Partial differential equations and finite difference methods in image processing--Part II: Image restoration

Linear Operators and Stochastic Partial Differential Equations in Gaussian Process Regression

“…The information can be encoded either by including a linear operator to the measurement model or by forming the prior covariance function as a solution to a stochastic partial differential equation (SPDE). Similar ideas have been previously used, for example, in Kriging [10][11][12][13][14], image processing [15,16,6], Kalman filtering [17,18], and physical inverse problems [19][20][21]. In the machine learning context, the inclusion of linear operators into GP regression models has also been previously proposed.…”

Interframe Adaptive Data Compression Techniques for Images.

“…From this statement it is clear that (A-2) would be a better model for most images. In [35] it has been demonstrated that the models which closely approximate (A-2) give much better performance in filtering images than that of (A-l).…”

“…A model based on a finite difference approximation of an elliptical partial differential equationreported in [34], and referred as NCU model filtering and data compression could be found in [35] and [75] respectively.…”

“…These values were found by a least squares fit of the model and the 16 x 16 measured covariances for the Girl image shown in Figure 6-10(a) [34,35]. For the measured covariance model of (A-5),the same Girl image data was used.…”

Spatial Autoregressions in Digital Image Restoration: Simultaneous Models.

“…The author is grateful to Prof. R. L. Kashyap Recently [6][7], stochastic representations of digital images by finite difference approximations of partial differential and elliptic systems, three different algorithms, viz., the causal, semicausal and noncausal algorithms, have been developed.…”