Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

Graph Wedgelets: Adaptive Data Compression on Graphs based on Binary Wedge Partitioning Trees and Geometric Wavelets

We introduce graph wedgelets - a tool for data compression on graphs based on the representation of signals by piecewise constant functions on adaptively generated binary graph partitionings. The adaptivity of the partitionings, a key ingredient to obtain sparse representations of a graph signal, is realized in terms of recursive wedge splits adapted to the signal. For this, we transfer adaptive partitioning and compression techniques known for 2D images to general graph structures and develop discrete variants of continuous wedgelets and binary space partitionings. We prove that continuous results on best m-term approximation with geometric wavelets can be transferred to the discrete graph setting and show that our wedgelet representation of graph signals can be encoded and implemented in a simple way. Finally, we illustrate that this graph-based method can be applied for the compression of images as well.Comment: 12 pages, 10 figure

Moments-Based Fast Wedgelet Transform

In the paper the moments-based fast wedgelet transform has been presented. In order to perform the classical wedgelet transform one searches the whole wedgelets’ dictionary to find the best matching. Whereas in the proposed method the parameters of wedgelet are computed directly from an image basing on moments computation. Such parameters describe wedgelet reflecting the edge present in the image. However, such wedgelet is not necessarily the best one in the meaning of Mean Square Error. So, to overcome that drawback, the method which improves the matching result has also been proposed. It works in the way that the better matching one needs to obtain the longer time it takes. The proposed transform works in linear time with respect to the number of pixels of the full quadtree decomposition of an image. More precisely, for an image of size N ×N pixels the time complexity of the proposed wedgelet transform is O(N2 log2 N)

The Multiplicative Zak Transform, Dimension Reduction, and Wavelet Analysis of LIDAR Data

This thesis broadly introduces several techniques within the context of timescale analysis. The representation, compression and reconstruction of DEM and LIDAR data types is studied with directional wavelet methods and the wedgelet decomposition. The optimality of the contourlet transform, and then the wedgelet transform is evaluated with a valuable new structural similarity index. Dimension reduction for material classification is conducted with a frame-based kernel pipeline and a spectral-spatial method using wavelet packets. It is shown that these techniques can improve on baseline material classification methods while significantly reducing the amount of data. Finally, the multiplicative Zak transform is modified to allow the study and partial characterization of wavelet frames

On the nonlinear statistics of range image patches

In [A. B. Lee, K. S. Pedersen, and D. Mumford, Int. J. Comput. Vis., 54 (2003), pp. 83–103], the authors study the distributions of 3 × 3 patches from optical images and from range images. In [G. Carlsson, T. Ishkanov, V. de Silva, and A. Zomorodian, Int. J. Comput. Vis., 76 (2008), pp. 1–12], the authors apply computational topological tools to the data set of optical patches studied by Lee, Pedersen, and Mumford and find geometric structures for high density subsets. One high density subset is called the primary circle and essentially consists of patches with a line separating a light and a dark region. In this paper, we apply the techniques of Carlsson et al. to range patches. By enlarging to 5×5 and 7×7 patches, we find core subsets that have the topology of the primary circle, suggesting a stronger connection between optical patches and range patches than was found by Lee, Pedersen, and Mumford

Transitions between states of magnetotail-ionosphere coupling and the role of solar wind dynamic pressure: the 25 July 2004 interplanetary CME case

In a case study, we investigate transitions between fundamental magnetosphere–ionosphere (M-I) coupling modes during storm-time conditions (SYM-H between −100 and −160 nT) driven by an interplanetary coronal mass ejection (ICME). We combine observations from the near tail, at geostationary altitude (GOES-10), and electrojet activities across the auroral oval at postnoon-to-dusk and midnight. After an interval of strong westward electrojet (WEJ) activity, a 3 h long state of attenuated/quenched WEJ activity was initiated by abrupt drops in the solar wind density and dynamic pressure. The attenuated substorm activity consisted of brief phases of magnetic field perturbation and electron flux decrease at GOES-10 near midnight and moderately strong conjugate events of WEJ enhancements at the southern boundary of the oval, as well as a series of very strong eastward electrojet (EEJ) events at dusk, during a phase of enhanced ring current evolution, i.e., enhanced SYM-H deflection within −120 to −150 nT. Each of these M-I coupling events was preceded by poleward boundary intensifications and auroral streamers at higher oval latitudes. We identify this mode of attenuated substorm activity as being due to a magnetotail state characterized by bursty reconnection and bursty bulk flows/dipolarization fronts (multiple current wedgelets) with associated injection dynamo in the near tail, in their braking phase. The latter process is associated with activations of the Bostrøm type II (meridional) current system. A transition to the next state of M-I coupling, when a full substorm expansion took place, was triggered by an abrupt increase of the ICME dynamic pressure from 1 to 5 nPa. The brief field deflection events at GOES-10 were then replaced by a 20 min long interval of extreme field stretching (Bz approaching 5 nT and Bx ≈ 100 nT) followed by a major dipolarization (Δ Bz ≈ 100 nT). In the ionosphere the latter stage appeared as a full-size stepwise poleward expansion of the WEJ. It thus appears that the ICME passage led to fundamentally different M-I coupling states corresponding to different levels of dynamic pressure (Pdyn) under otherwise very similar ICME conditions. Full WEJ activity, covering a wide latitude range across the auroral oval in the midnight sector, was attenuated by the abrupt dynamic pressure decrease and resumed after the subsequent abrupt increase

Graph-Cut Rate Distortion Algorithm for Contourlet-Based Image Compression

The geometric features of images, such as edges, are difficult to represent. When a redundant transform is used for their extraction, the compression challenge is even more difficult. In this paper we present a new rate-distortion optimization al-gorithm based on graph theory that can encode efficiently the coefficients of a critically sampled, non-orthogonal or even redundant transform, like the contourlet decomposition. The basic idea is to construct a specialized graph such that its min-imum cut minimizes the energy functional. We propose to ap-ply this technique for rate-distortion Lagrangian optimization in subband image coding. The method yields good compres-sion results compared to the state-of-art JPEG2000 codec, as well as a general improvement in visual quality. Index Terms — subband image coding, rate- distortion allocation 1