The dark channel prior (DCP) technique is an effective method to enhance hazy images. Dark channel is an image with the same size as the hazy image which represents the haze severity in different places of the image. The DCP method suffers from two problems: it is incapable for removing haze from smooth regions, causing blocking effects on these areas; it cannot properly reduce a haze with a no...

1 Alonzo Church, Ann. Math., 2nd ser., 33, 346-366 (1932), and 34, 839-864 (1933). S. C. Kleene, Ann. Math., 2nd ser., 35, 529-544 (1934). We shall refer to the latter paper as Kleene 1934. 2 Alonzo Church and J. B. Rosser, "Some Properties of Conversion." 3 Explicit formal definitions are given by S. C. Kleene, Amer. Jour. Math., 57, 153173 (1935). This paper, and a second part of it, forthcom...

In this paper, a novel second-order method based on change of variable and the symmetrical repeated quadrature formula is presented for numerical solving second kind Volterra integral equations with non-smooth solutions. Applying discrete Grönwall inequality weak singularity, convergence order O(N−2) in L∞ norm proved, where N refers to number time steps. Numerical results are conducted verify ...