In this paper, we study design of deep neural networks for tasks of image restoration. We propose a novel style of residual connections dubbed "dual residual connection", which exploits the potential of paired operations, e.g., up- and down-sampling or convolution with large- and small-size kernels. We design a modular block implementing this connection style; it is equipped with two containers to which arbitrary paired operations are inserted. Adopting the "unraveled" view of the residual networks proposed by , we point out that a stack of the proposed modular blocks allows the first operation in a block interact with the second operation in any subsequent blocks. Specifying the two operations in each of the stacked blocks, we build a complete network for each individual task of image restoration. We experimentally evaluate the proposed approach on five image restoration tasks using nine datasets. The results show that the proposed networks with properly chosen paired operations outperform previous methods on almost all of the tasks and datasets.
Haze removal Many studies assume the following model of haze: @math , where @math denotes a hazy scene image, @math is the true scene radiance (the clear image), @math is a transmission map, @math is global atmospheric light. The task is then to estimate @math , @math , and thus @math from the input @math @cite_53 @cite_43 @cite_8 @cite_44 @cite_36 . Recently, Zhang al @cite_44 proposed a method that uses CNNs to jointly estimate @math and @math , which outperforms previous approaches by a large margin. Ren al @cite_41 and Li al @cite_11 proposed method to directly estimate @math without explicitly estimating @math and @math . Yang al @cite_36 proposed a method that integrates CNNs to classical prior-based method.
@cite_8 @cite_36 @cite_41 @cite_53 @cite_44 @cite_43 @cite_11
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We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . Abstract Irregular sampling and stable sampling of band-limited functions have been studied by H.J. Landau [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 3752]. We prove that quasicrystals are sets of stable sampling. To cite this article: B. Matei, Y. Meyer, C. R. Acad. Sci. Paris, Ser. I 346 (2008). The concept of nearsightedeness of electronic matter (NEM) was introduced by W. Kohn in 1996 as the physical principal underlining Yang's electronic structure alghoritm of divide and conquer. It describes the fact that, for fixed chemical potential, local electronic properties at a point @math , like the density @math , depend significantly on the external potential @math only at nearby points. Changes @math of that potential, no matter how large , beyond a distance @math , have limited effects on local electronic properties, which tend to zero as function of @math . This remains true even if the changes in the external potential completely surrounds the point @math . NEM can be quantitatively characterized by the nearsightedness range, @math , defined as the smallest distance from @math , beyond which any change of the external potential produces a density change, at @math , smaller than a given @math . The present paper gives a detailed analysis of NEM for periodic met als and insulators in 1D and includes sharp, explicit estimates of the nearsightedness range. Since NEM involves arbitrary changes of the external potential, strong, even qualitative changes can occur in the system, such as the discretization of energy bands or the complete filling of the insulating gap of an insulator with continuum spectrum. In spite of such drastic changes, we show that @math has only a limited effect on the density, which can be quantified in terms of simple parameters of the unperturbed system. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. In the subgraph-freeness problem, we are given a constant-size graph @math , and wish to determine whether the network contains @math as a subgraph or not. The relaxation of the problem only requires us to distinguish graphs that are @math -free from graphs that are @math -far from @math -free, meaning an @math -fraction of their edges must be removed to obtain an @math -free graph. Recently, Censor-Hillel et. al. and showed that in the property-testing regime it is possible to test @math -freeness for any graph @math of size 4 in constant time, @math rounds, regardless of the network size. However, Fraigniaud et. al. also showed that their techniques for graphs @math of size 4 cannot test @math -cycle-freeness in constant time. In this paper we revisit the subgraph-freeness problem and show that @math -cycle-freeness, and indeed @math -freeness for many other graphs @math comprising more than 4 vertices, can be tested in constant time. We show that @math -freeness can be tested in @math rounds for any cycle @math , improving on the running time of @math of the previous algorithms for triangle-freeness and @math -freeness. In the special case of triangles, we show that triangle-freeness can be solved in @math rounds independently of @math , when @math is not too small with respect to the number of nodes and edges. We also show that @math -freeness for any constant-size tree @math can be tested in @math rounds, even without the property-testing relaxation. Building on these results, we define a general class of graphs for which we can test subgraph-freeness in @math rounds. This class includes all graphs over 5 vertices except the 5-clique, @math . For cliques @math over @math nodes, we We prove the existence of a polynomial time computable pseudorandom generator that @math -fools constant width regular read-once branching programs of length @math using a seed of length @math . The previous best pseudorandom generator for regular branching programs used a seed of length @math , and was due to Braverman et. al. and Brody and Verbin (FOCS 2010). Our pseudorandom generator is the INW generator due to Impagliazzo et. al. (STOC 1994). Our work shares some similarity with the recent work of Kouck ' y et. al. (STOC 2011)who get similar seed length for permutation branching programs. However, our work proceeds by analyzing the eigenvalues of the stochastic matrices that arise in the transitions of the branching program which arguably makes the technique more robust. As a corollary of our techniques, we present new results on the small biased spaces for group products'' problem by Meka and Zuckerman (RANDOM 2009). We get a pseudorandom generator with seed length @math . Previously, using the result of Kouck ' y et. al., it was possible to get a seed length of @math for this problem. In this work, we study indistinguishability obfuscation and functional encryption for general circuits: Indistinguishability obfuscation requires that given any two equivalent circuits @math and @math of similar size, the obfuscations of @math and @math should be computationally indistinguishable. In functional encryption, ciphertexts encrypt inputs @math and keys are issued for circuits @math . Using the key @math to decrypt a ciphertext @math yields the value @math but does not reveal anything else about @math . Furthermore, no collusion of secret key holders should be able to learn anything more than the union of what they can each learn individually. We give constructions for indistinguishability obfuscation and functional encryption that supports all polynomial-size circuits. We accomplish this goal in three steps: (1) We describe a candidate construction for indistinguishability obfuscation for @math circuits. The security of this construction is based on a new al...