19420160
Multiscale LMMSE-based image denoising with optimal wavelet selection
In this paper, a wavelet-based multiscale linear minimum mean square-error estimation (LMMSE) scheme for image denoising is proposed, and the determination of the optimal wavelet basis with respect to the proposed scheme is also discussed. The overcomplete wavelet expansion (OWE), which is more effective than the orthogonal wavelet transform (OWT) in noise reduction, is used. To explore the strong interscale dependencies of OWE, we combine the pixels at the same spatial location across scales as a vector and apply LMMSE to the vector. Compared with the LMMSE within each scale, the interscale model exploits the dependency information distributed at adjacent scales. The performance of the proposed scheme is dependent on the selection of the wavelet bases. Two criteria, the signal information extraction criterion and the distribution error criterion, are proposed to measure the denoising performance. The optimal wavelet that achieves the best tradeoff between the two criteria can be determined from a library of wavelet bases. To estimate the wavelet coefficient statistics precisely and adaptively, we classify the wavelet coefficients into different clusters by context modeling, which exploits the wavelet intrascale dependency and yields a local discrimination of images. Experiments show that the proposed scheme outperforms some existing denoising methods.
11758071
Algorithms for optimal multi-resolution quantization
Multi-resolution quantization is a way of constructing a progressively refinable description of a discrete random variable. The underlying discrete optimization problem is to minimize an expected distortion over all refinement levels weighted by the probability or importance of the descriptions of different resolutions. This research is motivated by the application of multimedia communications via variable-rate channels. We propose an O(rN2) time and O(N2 log N) space algorithm to design a minimum-distortion quantizer of r levels for a random variable drawn from an alphabet of size N. It is shown that for a very large class of distortion measures the objective function of optimal multi-resolution quantization satisfies the convex Monge property. The efficiency of the proposed algorithm hinges on the convex Monge property. But our algorithm is simpler (even though of the same asymptotic complexity) than the well-known SMAWK fast matrix search technique, which is the best existing solution to the quantization problem. For exponential random variables our approach leads to a solution of even lower complexity: O(rN) time and O(N log N) space, which outperforms all the known algorithms for optimal quantization in both multi- and single-resolution cases. We also generalize the multi-resolution quantization problem to a graph problem, for which our algorithm offers an efficient solution.
35689582
A fast recurring two-dimensional entropic thresholding algorithm
Thresholding is an important form of image segmentation and is used in the processing of images for many applications. One of the criteria to select a suitable threshold is the maximization of the two-dimensional (2-D) entropies based on the 2-D (gray-level/local average gray-level) histogram. The rationale of this approach is introduced. In order to reduce the computation time of entropy function, a fast recurring algorithm for 2-D entropic thresholding method is presented. The experimental results show that the processing time to obtain the threshold vector from 2-D histogram is reduced from 30 to 0.15 s.
20120387
Optimal Net Surface Problems with Applications
In this paper, we study an interesting geometric graph called multi-column graph in the d-D space (d ? 3), and formulate two combinatorial optimization problems called the optimal net surface problems on such graphs. Our formulations capture a number of important problems such as surface reconstruction with a given topology, medical image segmentation, and metric labeling. We prove that the optimal net surface problems on general d-D multicolumn graphs (d ? 3) are NP-hard. For two useful special cases of these d-D (d ? 3) optimal net surface problems (on the so-called proper ordered multi-column graphs) that often arise in applications, we present polynomial time algorithms. We further apply our algorithms to some surface reconstruction problems in 3-D and 4-D, and some medical image segmentation problems in 3-D and 4-D, obtaining polynomial time solutions for these problems. The previously best known algorithms for some of these applied problems, even for relatively simple cases, take at least exponential time. Our approaches for these applied problems can be extended to higher dimensions.
6198928
Energy-Efficient Deployment of Mobile Sensor Networks by PSO
Sensor deployment is an important issue in designing sensor networks. In this paper, particle swarm optimization (PSO) approach is applied to maximize the coverage based on a probabilistic sensor model in mobile sensor networks and to reduce cost by finding the optimal positions for the cluster-head nodes based on a well-known energy model. During the coverage optimization process, sensors move to form a uniformly distributed topology according to the execution of algorithm at base station. The simulation results show that PSO algorithm has faster convergence rate than genetic algorithm based method while achieving the goal of energy efficient sensor deployment.
11091243
Efficient Algorithms for Intensity Map Splitting Problems in Radiation Therapy
In this paper, we study several interesting intensity map splitting (IMSp) problems that arise in Intensity-Modulated Radiation Therapy (IMRT), a state-of-the-art radiation therapy technique for cancer treatments. In current clinical practice, a multi-leaf collimator (MLC) with a maximum leaf spread is used to deliver the prescribed intensity maps (IMs). However, the maximum leaf spread of an MLC may require to split a large intensity map into several abutting sub-IMs each being delivered separately, which results in prolonged treatment time. Few IM splitting techniques reported in the literature has addressed the issue of treatment delivery efficiency for large IMs. We develop a unified approach for solving the IMSp problems while minimizing the total beam-on time in various settings. Our basic idea is to formulate the IMSp problem as computing a k-link shortest path in a directed acyclic graph. We carefully characterize the intrinsic structures of the graph, yielding efficient algorithms for the IMSp problems.
42223547
Pairwise Data Clustering and Applications
Data clustering is an important theoretical topic and a sharp tool for various applications. Its main objective is to partition a given data set into clusters such that the data within the same cluster are "more" similar to each other with respect to certain measures. In this paper, we study the pairwise data clustering problem with pairwise similarity/ dissimilarity measures that need not satisfy the triangle inequality. By using a criterion, called the minimum normalized cut, we model the pairwise data clustering problem as a graph partition problem. The graph partition problem based on minimizing the normalized cut is known to be NP-hard. We present a ((4 + o(1)) ln n)-approximation polynomial time algorithm for the minimum normalized cut problem. We also give a more efficient algorithm for this problem by sacrificing the approximation ratio slightly. Further, our scheme achieves a ((2 + o(1)) ln n)- approximation polynomial time algorithm for computing the sparsest cuts in edge-weighted and vertex-weighted undirected graphs, improving the previously best known approximation ratio by a constant factor.