VistaRestoreTools1.0

  denoise In BayesShrink[5] we determine the threshold for each subband assuming a Generalized Gaussian Distribution(GGD) . The GGD is given by GG¾ X ¯ (x) = C(¾ X ¯ )exp¡ [® (¾ X ¯ )jxj]¯ (6) ¡ 1 < x < 1 ¯ > 0, where ® (¾ X ¯ ) = ¾ ¡ 1 X [ ¡ (3=¯ ) ¡ (1=¯ ) ]1=2 and C(¾ X ¯ ) = ¯ ¢ ® (¾ X ¯ ) 2¡ ( 1 ¯ ) and ¡ (t) = R1 0 e¡ uut¡ 1du. The parameter ¾ X is the standard deviation and ¯ is the shape parameter It has been observed[5] that with a shape parameter ¯ ranging from 0.5 to 1, we can describe the the distribution of coefficients in a subband for a large set of natural images.Assuming such a distribution for the wavelet coefficients, we empirically estimate ¯ and ¾ X for each subband and try to find the threshold T which minimizes the Bayesian Risk, i.e, the expected value of the mean square error.