This paper presents a novel approach to image denoising using adaptive principal components. Our assumptions are that the image is corrupted by additive white Gaussian noise. The new denoising technique performs well in terms of image visual fidelity, and in terms of PSNR values, the new technique compares very well against some of the most recently published denoising algorithms.

Image interpolation is a key aspect of digital image processing. This paper presents a novel interpolation method based on optimal recovery and adaptively determining the quadratic signal class from the local image behavior. The advantages of the new interpolation method are the ability to interpolate directly by any factor and to model properties of the data acquisition system into the algorithm itself. Through comparisons with other algorithms it is shown that the new interpolation is not only mathematically optimal with respect to the underlying image model, but visually it is very efficient at reducing jagged edges, a place where most other interpolation algorithms fail.

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The detection and estimation of machine vibration multiperiodic signals of unknown periods in white Gaussian noise is investigated. New estimates for the subsignals (signals making up the received signal) and their periods are derived using an orthogonal subspace decomposition approach. The concept of exactly periodic signals is introduced. This in turn simplifies and enhances the understanding of periodic signals.

Color images in single chip digital cameras are obtained by interpolating mosaiced color samples.These samples are encoded in a single chip CCD by sampling the light after it passes through a color filter array (CFA) that contains different color filters (i.e. red, green, and blue) placed in some pattern.The resulting sparsely sampled images of the three-color planes are interpolated to obtain the complete color image. Interpolation usually introduces color artifacts due to the phase-shifted, aliased signals introduced by the sparse sampling of the CFAs. This paper introduces a non-linear interpolation scheme based on edge information that produces high quality visual results. The new method is especially good at reconstructing the image around edges, a place where the visual human system is most sensitive.