Spatially adaptive wavelet thresholding with context modeling for image denoising
The method of wavelet thresholding for removing noise, or denoising, has been researched extensively due to its effectiveness and simplicity. Much of the literature has focused on developing the best uniform threshold or best basis selection. However, not much has been done to make the threshold values adaptive to the spatially changing statistics of images. Such adaptivity can improve the wavelet thresholding performance because it allows additional local information of the image (such as the identification of smooth or edge regions) to be incorporated into the algorithm. This work proposes a spatially adaptive wavelet thresholding method based on context modeling, a common technique used in image compression to adapt the coder to changing image characteristics. Each wavelet coefficient is modeled as a random variable of a generalized Gaussian distribution with an unknown parameter. Context modeling is used to estimate the parameter for each coefficient, which is then used to adapt the thresholding strategy. This spatially adaptive thresholding is extended to the overcomplete wavelet expansion, which yields better results than the orthogonal transform. Experimental results show that spatially adaptive wavelet thresholding yields significantly superior image quality and lower MSE than the best uniform thresholding with the original image assumed known.

title: Adaptive wavelet thresholding for image denoising and compression
abstract: The first part of this paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing applications. The proposed threshold is simple and closed-form, and it is adaptive to each subband because it depends on data-driven estimates of the parameters. Experimental results show that the proposed method, called BayesShrink, is typically within 5% of the MSE of the best soft-thresholding benchmark with the image assumed known. It also outperforms SureShrink (Donoho and Johnstone 1994, 1995; Donoho 1995) most of the time. The second part of the paper attempts to further validate claims that lossy compression can be used for denoising. The BayesShrink threshold can aid in the parameter selection of a coder designed with the intention of denoising, and thus achieving simultaneous denoising and compression. Specifically, the zero-zone in the quantization step of compression is analogous to the threshold value in the thresholding function. The remaining coder design parameters are chosen based on a criterion derived from Rissanen's minimum description length (MDL) principle. Experiments show that this compression method does indeed remove noise significantly, especially for large noise power. However, it introduces quantization noise and should be used only if bitrate were an additional concern to denoising.

title: Wavelet thresholding via MDL for natural images
abstract: We study the application of Rissanen's (1989) principle of minimum description length (MDL) to the problem of wavelet denoising and compression for natural images. After making a connection between thresholding and model selection, we derive an MDL criterion based on a Laplacian model for noiseless wavelet coefficients. We find that this approach leads to an adaptive thresholding rule. While achieving mean-squared-error performance comparable with other popular thresholding schemes, the MDL procedure tends to keep far fewer coefficients. From this property, we demonstrate that our method is an excellent tool for simultaneous denoising and compression. We make this claim precise by analyzing MDL thresholding in two optimality frameworks; one in which we measure rate and distortion based on quantized coefficients and one in which we do not quantize, but instead record rate simply as the number of nonzero coefficients.

title: A rate of convergence result for a universal D-semifaithful code
abstract: The problem of optimal rate universal coding is considered in the context of rate-distortion theory. A D-semifaithful universal coding scheme for discrete memoryless sources is given. The main result is a refined covering lemma based on the random coding argument and the method of types. The average codelength of the code is shown to approach its lower bound, the rate-distortion function, at a rate O(n/sup -1/log n), and this is conjectured to be optimal based on a result of A.J. Pilc (1968). Issues of constructiveness and universality are addressed.

title: The Minimum Description Length Principle in Coding and Modeling
abstract: We review the principles of minimum description length and stochastic complexity as used in data compression and statistical modeling. Stochastic complexity is formulated as the solution to optimum universal coding problems extending Shannon's basic source coding theorem. The normalized maximized likelihood, mixture, and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms. We assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference. Context tree modeling, density estimation, and model selection in Gaussian linear regression serve as examples.

title: Wavelet thresholding for multiple noisy image copies
abstract: This correspondence addresses the recovery of an image from its multiple noisy copies. The standard method is to compute the weighted average of these copies. Since the wavelet thresholding technique has been shown to effectively denoise a single noisy copy, we consider in this paper combining the two operations of averaging and thresholding. Because thresholding is a nonlinear technique, averaging then thresholding or thresholding then averaging produce different estimators. By modeling the signal wavelet coefficients as Laplacian distributed and the noise as Gaussian, our investigation finds the optimal ordering to depend on the number of available copies and on the signal-to-noise ratio. We then propose thresholds that are nearly optimal under the assumed model for each ordering. With the optimal and near-optimal thresholds, the two methods yield similar performance, and both show considerable improvement over merely averaging.

title: Scalable and reliable data delivery in mobile ad hoc sensor networks
abstract: This paper studies scalable data delivery algorithms in mobile ad hoc sensor networks with node and link failures. Many algorithms have been developed for data delivery and fusion in static microsensor networks, but most of them are not appropriate for mobile sensor networks due to their heavy traffic and long latency. In this paper we propose an efficient and robust data delivery algorithm for distributed data fusion in mobile ad hoc sensor networks, where each node controls its data flows and learns routing decisions solely based on their local knowledge. We analyze the localized algorithm in a formal model and validate our model using simulations. The experiments indicate that controlled data delivery processes significantly increase the probability of relevant data being fused in the network even with limited local knowledge of each node and relatively small hops of data delivery.

title: Adaptive Query Processing in Point-Transformation Schemes
abstract: Point-transformation schemes transform multidimensional points to one-dimensional values so that conventional access methods can be used to index multidimensional points, enabling convenient integration of multidimensional query facilities into complex transactional database management systems. However, in high-dimensional data spaces, the computational complexity of the required query transformation is prohibitive. This paper proposes a near-optimal solution based on our novel ideas of adaptive Z-ordering. The experimental results show that the proposed approach significantly improves the query performance of point-transformation schemes. The idea can easily be generalized to accommodate any hierarchical space-filling curve, not just the Z-curve.

title: Intelligent online BGP-4 analyzer
abstract: Border Gateway Protocol 4 (BGP-4) is one of the widely used routing protocols. This paper presents the design and implementation of an intelligent BGP-4 analyzer working online. Serving in the study and test of BGP-4, the analyzer can capture all the BGP-4 traffic and further exploit "state synchronization" algorithm to analyze the behavior of the BGP-4 state machine by observing the interaction between BGP-4 peers. As to the routing information manipulation, the analyzer can also verify its correctness and efficiency through internal process simulation and statistical computation. And the interested sessions and routes are traced and analyzed. This analyzer possesses many other beneficial features and plays an important role both in the study and test of BGP-4 and the network management.

title: Dynamic Splitting Policies of the Adaptive 3DR-Tree for Indexing Continuously Moving Objects
abstract: Moving-objects databases need a spatio-temporal indexing scheme for moving objects to efficiently process queries over continuously changing locations of the objects. A simple extension of the R-tree that employs time as the third dimension of the data universe shows low space utilization and poor search performance because of overlapping index regions. In this paper, we propose a variant of the 3-dimensional R-tree called the Adaptive 3DR-tree. The dynamic splitting policies of the Adaptive 3DR-tree significantly reduce the overlap rate, and this, in turn, results in improved query performance. The results of our extensive experiments show that the Adaptive 3DR-tree outperforms the original 3D R-tree and the TB-tree typically by a big margin.

title: An Efficient Zoning Technique for Multi-dimensional Access Methods
abstract: In emerging database applications that deal with large sets of multidimensional data, the performance of the query system significantly depends on the performance of its access methods and the underlying disk system. In recent years, hard disks are manufactured with multiple physical zones, where seek times and data transfer rates vary significantly across the zones. However, there is a marked lack of investigation on how to optimize multidimensional access methods given a zoned disk model. The paper proposes a novel dynamic zoning technique called DMD-Zoning that can be applied to a variety of multidimensional access methods and that can fully utilize zoning characteristics of hard disks for busy multi-user database systems.