Dichteschätzung mit Wavelets

Es soll eine Dichtefunktion geschätzt werden unter der Modellannahme, dass diese in einer geeigneten Besovklasse liegt und kompakten Träger hat. Hierzu wird ein Waveletschätzer TW näher untersucht, der Thresholding-Methoden verwendet. Es wird die asymptotische Konvergenzgeschwindigkeit von TW für eine große Zahl von Beobachtungen angegeben und bewiesen. Schließlich werden in einem Überblick weitere Waveletschätzer diskutiert und mit TW verglichen. Es zeigt sich, dass TW in vielen Modellannahmen die optimale Konvergenzrate erreicht.

Scoring-thresholding pattern based text classifier

A big challenge for classification on text is the noisy of text data. It makes classification quality low. Many classification process can be divided into two sequential steps scoring and threshold setting (thresholding). Therefore to deal with noisy data problem, it is important to describe positive feature effectively scoring and to set a suitable threshold. Most existing text classifiers do not concentrate on these two jobs. In this paper, we propose a novel text classifier with pattern-based scoring that describe positive feature effectively, followed by threshold setting. The thresholding is based on score of training set, make it is simple to implement in other scoring methods. Experiment shows that our pattern-based classifier is promising.

Spatiotemporal segmentation based on two-dimensional spatiotemporal entropic thresholding

A novel spatiotemporal segmentation technique is further developed for extracting uncovered background and moving objects from the image sequences, then the following motion estimation is performed only on the regions corresponding to moving objects. The frame difference contrast (FCON) and local variance contrast (LCON), which are related to the temporal and spatial homogeneity of the image sequence, are selected to form the 2-D spatiotemporal entropy. Then the spatial segmentation threshold is determined by maximizing the 2-D spatiotemporal entropy, and the temporal segmentation point is selected to minimize the complexity measure for image sequence coding. Since both temporal and spatial correlation of an image sequence are exploited, this proposed spatiotemporal segmentation technique can further be used to determine the positions of reference frames adaptively, hence resulting in a low bit rate. Experimental results show that this segmentation-based coding scheme is more efficient than usual fixed-size coding algorithms. (C) 1997 Society of Photo-Optical Instrumentation Engineers.

Improved bounds for subband-adaptive iterative shrinkage/thresholding algorithms.

This paper presents new methods for computing the step sizes of the subband-adaptive iterative shrinkage-thresholding algorithms proposed by Bayram & Selesnick and Vonesch & Unser. The method yields tighter wavelet-domain bounds of the system matrix, thus leading to improved convergence speeds. It is directly applicable to non-redundant wavelet bases, and we also adapt it for cases of redundant frames. It turns out that the simplest and most intuitive setting for the step sizes that ignores subband aliasing is often satisfactory in practice. We show that our methods can be used to advantage with reweighted least squares penalty functions as well as L1 penalties. We emphasize that the algorithms presented here are suitable for performing inverse filtering on very large datasets, including 3D data, since inversions are applied only to diagonal matrices and fast transforms are used to achieve all matrix-vector products.

Sparse recovery of complex phase-encoded velocity images using iterative thresholding

In this paper we propose a new algorithm for reconstructing phase-encoded velocity images of catalytic reactors from undersampled NMR acquisitions. Previous work on this application has employed total variation and nonlinear conjugate gradients which, although promising, yields unsatisfactory, unphysical visual results. Our approach leverages prior knowledge about the piecewise-smoothness of the phase map and physical constraints imposed by the system under study. We show how iteratively regularizing the real and imaginary parts of the acquired complex image separately in a shift-invariant wavelet domain works to produce a piecewise-smooth velocity map, in general. Using appropriately defined metrics we demonstrate higher fidelity to the ground truth and physical system constraints than previous methods for this specific application. © 2013 IEEE.

Thresholding of noisy shoeprint images based on pixel context

In a typical shoeprint classification and retrieval system, the first step is to segment meaningful basic shapes and patterns in a noisy shoeprint image. This step has significant influence on shape descriptors and shoeprint indexing in the later stages. In this paper, we extend a recently developed denoising technique proposed by Buades, called non-local mean filtering, to give a more general model. In this model, the expected result of an operation on a pixel can be estimated by performing the same operation on all of its reference pixels in the same image. A working pixel’s reference pixels are those pixels whose neighbourhoods are similar to the working pixel’s neighbourhood. Similarity is based on the correlation between the local neighbourhoods of the working pixel and the reference pixel. We incorporate a special instance of this general case into thresholding a very noisy shoeprint image. Visual and quantitative comparisons with two benchmarking techniques, by Otsu and Kittler, are conducted in the last section, giving evidence of the effectiveness of our method for thresholding noisy shoeprint images.

Image Denoising Using Sure-Based Adaptive Thresholding In Directionlet Domain

The standard separable two dimensional wavelet transform has achieved a great success in image denoising applications due to its sparse representation of images. However it fails to capture efficiently the anisotropic geometric structures like edges and contours in images as they intersect too many wavelet basis functions and lead to a non-sparse representation. In this paper a novel de-noising scheme based on multi directional and anisotropic wavelet transform called directionlet is presented. The image denoising in wavelet domain has been extended to the directionlet domain to make the image features to concentrate on fewer coefficients so that more effective thresholding is possible. The image is first segmented and the dominant direction of each segment is identified to make a directional map. Then according to the directional map, the directionlet transform is taken along the dominant direction of the selected segment. The decomposed images with directional energy are used for scale dependent subband adaptive optimal threshold computation based on SURE risk. This threshold is then applied to the sub-bands except the LLL subband. The threshold corrected sub-bands with the unprocessed first sub-band (LLL) are given as input to the inverse directionlet algorithm for getting the de-noised image. Experimental results show that the proposed method outperforms the standard wavelet-based denoising methods in terms of numeric and visual quality