Plenoptic imaging systems are often used for applications like refocusing, multimodal imaging, and multiview imaging. However, their resolution is limited to the number of lenslets. In this paper we investigate paraxial, incoherent, plenoptic image formation, and develop a method to recover some of the resolution for the case of a two-dimensional (2D) in-focus object. This enables the recovery of a conventional-resolution, 2D image from the data captured in a plenoptic system. We show simulation results for a plenoptic system with a known response and Gaussian sensor noise.
In this paper, we study a generalization of the Donoho-Johnstone denoising model for the case of the translation-invariant wavelet transform. Instead of softthresholding coefficients of the classical orthogonal discrete wavelet transform, we study soft-thresholding of the coefficients of the translation-invariant discrete wavelet transform. This latter transform is not an orthogonal transformation. As a first step, we construct a level-dependent threshold to remove all the noise in the wavelet domain. Subsequently, we use the theory of interpolating wavelet transforms to characterize the smoothness of an estimated denoised function. Based on the fact that the inverse of the translation-invariant discrete transform includes averaging over all shifts, we use smoother autocorrelation functions in the representation of the estimated denoised function in place of Daubechies scaling functions. 2002 Elsevier Science
-Two methods for analyzing graphs such as those occurring in the stock market, geographical profiles and rough surfaces, are investigated. They are based on different scaling laws for the distributions of jumps as a function of the lag. The first is a large deviation analysis, and the second is based on the concept of a self-similar process introduced by Mandelbrot and van Ness. We show that large deviation analysis does not apply to either the stock market nor fractional Brownian motion (H = 0.5). Instead the analysis based on self-similarity is applicable to both, and does indicate that especially the negative log-price fluctuations have a large degree of self-similarity. The latter analysis allows one to probe the degree of self-similarity of a process, beyond what is possible with the exponent H typically used to describe self-affine graphs.
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