We study various approximation classes associated with m-term approximation by elements from a (possibly redundant) dictionary in a Banach space. The standard approximation class associated with the best m-term approx...
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We study various approximation classes associated with m-term approximation by elements from a (possibly redundant) dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove that assuming a certain structure Of the dictionary is sufficient and (almost) necessary to obtain stronger results. We give examples of classical dictionaries in L-p spaces and modulation spaces where our results recover some known Jackson type estimates, and discuss some new estimates they provide.
We propose a fast pairwise nearest neighbor (PNN)-based O(N log N) time algorithm for multilevel nonparametric thresholding, where N denotes the size of the image histogram. The proposed PNN-based multilevel threshold...
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We propose a fast pairwise nearest neighbor (PNN)-based O(N log N) time algorithm for multilevel nonparametric thresholding, where N denotes the size of the image histogram. The proposed PNN-based multilevel thresholding algorithm is considerably faster than optimal thresholding. On a set of 8 to 16 bits-per-pixel real images, experimental results also reveal that the proposed method provides better quality than the Lloyd-Max quantizer alone. Since the time complexity of the proposed thresholding algorithm is log linear, it is applicable in real-time image processing applications. (C) 2003 SPIE and IST.
This paper presents an adaptive raster-scan thresholding algorithm which can deal with an image acquired under imperfect illumination. A statistical measurement called LSSD (Largest Static State Difference) relating t...
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This paper presents an adaptive raster-scan thresholding algorithm which can deal with an image acquired under imperfect illumination. A statistical measurement called LSSD (Largest Static State Difference) relating to the gray-level variation is found first, According to the measurement, the pixels are separated into static and transient states which are treated by two different procedures, respectively. A hardware implementation of this algorithm shows that the real-time requirement can be met. Experiments of applying this algorithm to extracting characters from documents confirmed that a reasonable binary image can be efficiently and effectively obtained from a gray-level image under various illuminations.
A new technique for automatic channel characterisation and selection in spectrally congested environments, known as `template correlation??, is described. Its performance under simulated conditions is illustrated. Mod...
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A new technique for automatic channel characterisation and selection in spectrally congested environments, known as `template correlation??, is described. Its performance under simulated conditions is illustrated. Modification of the basic technique to reduce the computational load, via a thresholding algorithm, is also discussed.
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