Reconstruction is prerequisite whenever a discrete signal needs to be resampled as a result of transformation such as texture mapping, image manipulation, volume slicing. and rendering. We present a new method for the characterization and measurement of reconstruction error in spatial domain. Our method uses the Classical Shannon’s Sampling Theorem as a basis to develop error bounds. We use thi...

Digital speech transmission systems use source coding to reduce the bit rate and channel coding to correct transmission errors. Furthermore, in periods of a very poor channel quality error concealment of residual bit errors becomes necessary as channel decoding fails. However, if the channel is clear, channel coding would not be required at all and the speech quality could be improved by allowi...

Prior results on input reconstruction for multi-input, multi-output discretetime linear systems are extended by defining l-delay input and initial-state observability. This property provides the foundation for reconstructing both unknown inputs and unknown initial conditions, and thus is a stronger notion than l-delay left invertibility, which allows input reconstruction only when the initial s...

This paper evaluates the final reconstruction quality of 3D objects from different reconstruction methods by comparing rendered views of a 3D model to the original views, initially taken from 2D cameras. The paper uses pixel-by-pixel error measures, like pixelwise reconstruction error for non-textured objects and PSNR values for colored or textured objects. Concurrently, the limitations of such...

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 rendering. 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 tim...

Recently, many l1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed....