Comparison of Canonical SVD and penalised SVD

  • On figure 1 is shown an example (given as demo in the package) of an SVD using penalisations. Using penalisations means the components are constrained to lie into given spaces (e.g. Sobolev space).The reconstruction of the image (with added noise) using some smooth components is compared to the reconstruction using canonical svd algorithm.

    This is in the demo (in PTAk):

    >demo.SVDgen(snr=3,openX11s=T)

    where snr is defined as te range of te original image divided by the standard deviation of the Gaussian noise added.

    in the demo is called SVDgen

    smoofun <- rep(list(Susan1D),7)

    d.svdo <- SVDgen(timage12,nomb=25,smoothing=TRUE,smoo =list(smoofun))

    The smoother in each the x and y orientations is a combination of a kernel regression (i.e."physical" neighbours) and non-linear kernels moothing (i.e. value neighbours).

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    Didier Leibovici
    Last modified: Thu Jul 5 16:11:48 BST 2001