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Theory and Applications of Speckle Displacement and Decorrelation
Published in Rajpal S. Sirohi, Speckle Metrology, 2020
We have discussed the dynamic properties of laser speckles that are caused by displacement or deformation of diffusely reflecting surfaces. They can be quantitatively described in terms of the cross-correlation function of the intensity distributions at an observation plane before and after the surface movement. This function has been derived for the diffraction field (free-space geometry) and the image field including the defocused region by using the Fresnel-Kirchhoff diffraction formula. The cross-correlation shows a peak whose position corresponds to speckle displacement and whose height indicates speckle decorrelation accompanying the displacement. The dependence of the speckle displacement on individual deformation parameters such as translation, rotation, and strain as well as on optical configurations has been explicitly presented. Displacement is caused by the change in the phase relationship of the superposed wavelets, while decorrelation is related to the walk-off of the surface region out of the incident laser spot or of the speckle out of the imaging area of the lens.
Artifact Reduction by Post-Processing in Image Compression
Published in H.R. Wu, K.R. Rao, Digital Video Image Quality and Perceptual Coding, 2017
Transform-based compression is by far the most popular choice in image and video coding. Due to its near-optimal decorrelation and energy compaction properties and the availability of fast algorithms and hardware implementations, the discrete cosine transform (DCT) [RY90, Jai89] is the dominant one among various transforms. As a result, the block-based DCT is recommended and used in most of the current image and video compression standards, such as the JPEG [PM93], the MPEG-1/2/4 [J. 96], and the H.261/2/3 [Gha03, ITU98]. In transform based compression, the image is transformed to a domain significantly different from the image intensity (spatial domain) [NH94, Cla85]. This is achieved by transforming blocks of data by a linear transformation. It is well known that, at low bit rates, a major problem associated with the BDCT compression is that the reconstructed images manifest visually objectionable artifacts [YW98]. One of the best known artifacts in low bit rate transform coded images appears as the blocking effect, which is noticeable especially in the form of undesirable conspicuous block boundaries.
Ultrafast optoelectronics
Published in John P. Dakin, Robert G. W. Brown, Handbook of Optoelectronics, 2017
Unfortunately, no way exists to retrieve the original pulse profile from any measured autocorrelation traces without additional knowledge. Being inspired by an expected theoretical description of the mode-locking process, one can sometimes assume an expected pulse shape and then retrieval is simple. This is, unfortunately, not a valid assumption in the sub-10 fs regime with its complex pulse shapes. In this regime, simple analytical functions can no longer be assumed for decorrelation of the measured autocorrelation function. Additionally, the sub-10 fs regime is very demanding, and pulse shaping by spectral filtering or dispersion in the beam splitters and nonlinear crystal has to be kept to a minimum. Wherever possible, this regime calls for the use of metal-coated reflective optics.
Multivariate geostatistical simulation with PPMT: an application for uncertainty measurement
Published in Applied Earth Science, 2021
Paulo Henrique Faria, João Felipe Coimbra Leite Costa, Marcel Antônio Arcari Bassani
Two well-known decorrelation methods are Principal Component Analysis (PCA) (Pearson 1901) and Minimum/Maximum Autocorrelation Factors (MAF) (Switzer and Green 1984; Desbarats and Dimitrakopoulos 2000). These methods work well when the data have linear relationships. In this context, they do not apply to data with complex relations. This issue motivated the development of techniques that enable multi-Gaussian transformations, such as Stepwise Conditional Transformation, which guarantees multi-Gaussian transformed variables with zero correlation (Leuangthong and Deutsch 2003). These authors explain that this method has limitations regarding the quantity of data, mentioning a general rule of 10n to 20n data (where n is the number of variables) to achieve well-discretised distributions. To enable working with complex correlated data and any number of variables, Barnett et al. (2014) proposed the Projection Pursuit Multivariate Transform (PPMT), which allows a complete decorrelation and multi-Gaussian transformation of the dataset. Several works demonstrating the applicability of PPMT for multivariate geostatistical simulation are reported in the literature (Bassani et al. 2018; Battalgazy and Madani 2019).