Formulas for estimating the probability of failure when testing reveals no errors are introduced. These formulas incorporate random testing results, information about the input distribution; and prior assumptions about the probability of failure of the software. The formulas are not restricted to equally likely input distributions, and the probability of failure estimate can be adjusted when assumptions about the input distribution change. The formulas are based on a discrete sample space statistical model of software and include Bayesian prior assumptions. Reusable software and software in life-critical applications are particularly appropriate candidates for this type of analysis.>

An algorithm is developed for defining small kernels that are conditioned on the important components of the imaging process: the nature of the scene, the point-spread function of the image-gathering device, sampling effects, noise, and post-filter interpolation. Subject to constraints on the spatial support of the kernel, the algorithm generates the kernal values that minimize the expected mean-square error of the estimate of the scene characteristic. This development is consistent with the derivation of the spatially unconstrained Wiener characteristic filter, but leads to a small, spatially constrained convolution kernel. Simulation experiments demonstrate that the algorithm is more flexible than traditional small-kernel techniques and yields more accurate estimates.>

Most digital image restoration algorithms are inherently incomplete because they are conditioned on a discrete-input, discrete-output model which only accounts for blurring during image gathering and additive noise. For those restoration applications where sampling and reconstruction (display) are important the restoration algorithm should be based on a more comprehensive end-to-end model which also accounts for the potentially important noise-like effects of aliasing and the low- pass filtering effects of interpolative reconstruction. In this paper we demonstrate that, although the mathematics of this more comprehensive model is more complex, the increase in complexity is not so great as to prevent a complete development and analysis of the associated minimum mean- square error (Wiener) restoration filter. We also survey recent results related to the important issue of implementing this restoration filter, in the spatial domain, as a computationally efficient small convolution kernel.