International audienc

An algorithm for denoising image based on directionalet is proposed, and in each high-frequency subbands, adaptive Wiener filtering (window size 25 1× ) is performed. Then, the denoised image is obtained by reconstruction from the filtered coefficients. At last, all directional sub-images are averaged.. The experiments results showed that this method outperforms Wiener filtering in standard 2-D wavelet domain. The SNR is improved 1~3dB.

We prove that the numerical invariant [Formula: see text] of a reduced irreducible plane curve singularity germ is non-negative, non-decreasing under blowups and strictly increasing unless the curve is non-singular. This provides a new perspective to understand the question posed by Dimca and Greuel. Moreover, our work can be put in the general framework of discovering monotonic invariants under blowups.

Abstract. For a line arrangement A in the complex projective plane P , we investigate the compacti cation F in P of the a ne Milnor ber F and its minimal resolutioñ F. We compute the Chern numbers ofF in terms of the combinatorics of the line arrangement A. As applications of the computation of the Chern numbers, we show that the minimal resolution is never a quotient of a ball; in addition, we also prove thatF is of general type when the arrangement has only nodes or triple points as singularities; nally, we compute all the Hodge numbers of someF by using some knowledge about the Milnor ber monodromy of the arrangement.

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