Variables and structures

If parameters are not set, default values are used. For example

OIDATA,PDATA =  painter()

calls painter with all default values.

Variables

These two variables cannot be included in OIDATA structure.

  • nbitermax: number of ADMM iterations. Default: 1000.
  • aff: if aff=true plots are enabled using PyPlot.jl. Default: false.

Variables in OIDATA structure

The structure OIDATA contains all OIFITS information and user defined parameters.

Execution Variables:

  • admm: if admm=false the function only initializes the structures. The function painter can be used after to iterate the ADMM algorithm. Default: true.
  • CountPlot: draw plot at each CountPlot iterations. Default: 10.
  • PlotFct: is a user defined function which is called at each CountPlot iterations. This function must respect the input argument of painterplotfct function and must call PyPlot, see Examples and demo section. Default: painterplotfct.

Initialization and initial estimate:

  • autoinit: if autoinit=true some parameters are automatically set or rescaled. Default: true.

The parameters which are automaticaly initialized are alpha, beta, rho_y_xi and rho_y_gamma. They corresponds to parameters related to proximal operator for squared visibilities and for phases differences. Regularization parameters lambda_spat and lambda_spec are rescaled to be invariant with user parameters. lambda_spat is divided by the number of pixels and lambda_spec by the number of wavelength. The total flux is also normalized to allow the use of almost predefined parameters. The initial estimate is rescaled by the flux of the data.

Data and image related variables:

  • Folder: path to the folder containing OIFITS/FITS files. Default: ./OIFITS. If ./OIFITS does not exists src/OIFITS in PAINTER.jl/ default installation folder, containing FITS files for the demo, is used.

  • indfile: allows to chose the set of OIFITS/FITS files in Folder that will be processed. indfile is an Array{Int64,1} containing the indexes of the files in alphabetical order. Default: all files.

  • indwvl: allows to chose the set of processed wavelengths. indwvl is an Array{Int64,1} containing the indexes of the wavelengths in increasing order. Default: all wavelengths.

  • nx: image size in pixels (the size of the image is nx2). Default: 64.

  • FOV: Field Of View of the reconstructed image in ArcSecond. Default: 40e-3.

  • mask3D: Binary mask defining the support constraint. mask3D can be:

    • a path to a FITS file,
    • an Array,
    • an empty Array (no constraint).

    mask3D can be set by the function mask. Default: no constraint.

  • xinit3D: Initial estimate of the object or of the complex visibilities. xinit3D can be:

    • a path to a FITS files containing the object,
    • an Array containing the object,
    • and Array containing the complex visibilities.

    Default: centered Dirac functions at all wavelengths.

  • dptype define the kind of matrix difference used to generate differential phase, can be parameterized by dpprm :

    • "all" the difference between the first wavelength and all others (1-2, 1-3, ...), see Eqs. 35
    • "diag" the difference between all consecutive wavelengths (1-2, 2-3, ...)
    • "ref" the same as "all" but with a reference channel defined by dpprm, the same as "all" if ``dpprm``=1
    • "frame" the difference between wavelength are performed inside non overlapping window with a size dpprm
    • "sliding" the difference between wavelength are performed using a sliding window with a size dpprm

    Default: if not given the default matrix difference is "all", for details about other methods see [3].

ADMM algorithm parameters:

  • alpha: weight for squared visibilities modulus data fidelity term, see Eqs. 25, 31 in [1]. Default: 1.
  • beta: weight for phases (closures and differential) data fidelity term, see Eqs. 25,31 in [1]. Default: 1.
  • lambda_spat: Spatial regularization parameter, see Eqs. 29, 31 in [1]. Default: nx-2.
  • lambda_spec: Spectral regularization parameter, see Eqs. 29, 31 in [1]. Default: 1e-2.
  • rho_y: ADMM parameter for data fidelity,see Eqs. 35, 50-52 in [1]. Default: 10.
  • rho_spat: ADMM parameter for Spatial regularization, see Eqs. 25, 31 in [1]. Default: 1, (0 to disable).
  • rho_spec: ADMM parameter for Spectral regularization, see Eqs. 42, 55 in [1]. Default: 1, (0 to disable).
  • rho_ps: ADMM parameter for positivity constraint, see Eq. 47, 54 in [1]. Default: 1, (0 to disable).
Secondary or specific paramaters:

The defaults values of these parameteres are tuned for the general cases. Nevertheless, the user may modified them for specific applications.

  • lambda_L1: regularization parameter for an l1 constraint on the image. l1 constraint emphasizes sparsity of objects (e.g. stars field). Default: 0.
  • Wvlt: array of wavelets basis for spatial regularization, see [2]. See Wavelets.jl for definitions. Default: first 8 Daubechies wavelets and Haar wavelets. Wvlt = [WT.db1, WT.db2, WT.db3, WT.db4, WT.db5, WT.db6, WT.db7, WT.db8, WT.haar].
  • epsilon: Ridge/Tikhonov regularization parameter, see Eqs. 29, 31 in [1]. Default: 1e-6.
  • eps1: stopping criterium for primal residual in ADMM algorithm. Default: 1e-6.
  • eps2: stopping criterium for dual residual in ADMM algorithm. Default: 1e-6.

Constant in OIDATA structure

The structure OIDATA: contains also constants related to the data and extracted from OIFITS files.

  • nb: number of bases.
  • nw: number of wavelength.
  • U: the U spatial frequencies matrix.
  • V: the V spatial frequencies matrix.
  • P: squared visibilities Matrix.
  • W: squared visibilities variance Matrix.
  • T3: phases closure matrix.
  • T3err: phases closure variance matrix.
  • DP: differential phases vector.
  • DPerr: differential phases variance vector.
  • Xi: dictionary of phases difference Vector.
  • K: dictionary of phases difference variance vector.

For matrices, the column index is associated to the wavelength index.

Variables in PDATA structure

Useful outputs in the structure PDATA are:

  • PDATA.x: the reconstructed 3D images !
  • PDATA.w: positivity and support constraint. These constraints can be applied to PDATA.x with PDATA.x.*(PDATA.w.>0).
  • PDATA.Fx: non uniform Fourier transform of the reconstructed 3D images.
  • PDATA.H: dictionary of phases to phases differences sparse matrix.
  • PDATA.crit1: the primal residual of the ADMM algorithm.
  • PDATA.crit2: the dual residual of the ADMM algorithm.
  • PDATA.ind: number of iterations, useful to re-run algorithm.

References

[1](1, 2, 3, 4, 5, 6, 7, 8, 9) Schutz, A., Ferrari, A., Mary, D. Soulez, F., Thiébaut, E., Vannier, M. “PAINTER: a spatio-spectral image reconstruction algorithm for optical interferometry”. JOSA A. Vol. 31, Iss. 11, pp. 2356–2361, (2014). arXiv
[2]Schutz, A., Ferrari, A., Mary, D., Thiébaut, E., Soulez, F. “Large scale 3D image reconstruction in optical interferometry”. EUSIPCO, 2015, Nice. arXiv
[3]Schutz, A., Ferrari, A., Thiébaut, E., Soulez, F., Vannier, M., Mary D. “Interbands phase models for polychromatic image reconstruction in optical interferometry”. SPIE, 2016, Edinburgh.