Help for "shapelets_recomp" routine:

Transform back from shapelets and realise a pixellated image.

This routine is the opposite of shapelets_decomp.pro. It takes a list of shapelet coefficients (stored within a decomp structure with various other meta-parameters) and generates a pixellated image. The returned variable recomp is a 2D floating point array of flux values within pixels.

The decomp structure itself stores flags that determine e.g. whether the basis functions are evaluated at the centres of pixels or integrated within them (by default, it uses the same configuration as was used to initially decompose the object using shapelets_decomp.pro). A few more options are available. For example, top=10 can be specified to use only the ten shapelet coefficients with the largest absolute values during the reconstruction. This was used to investigate data compression rates for the Shapelets: I paper.

See also the header below, which has been extracted from the source code for this routine.

; NAME:
;      SHAPELETS_RECOMP
;
; CATEGORY:
;      Shapelets.
;
; PURPOSE:
;      Compute the recomposed image corresponding to a set of shapelet
;      coefficients calculated using shapelets_decomp.pro. The input decomp
;      structure also contains a few meta-parameters, including the shapelet
;      scale size beta, and whether or not the basis functions should be
;      integrated within pixels, or merely evaluated at the centre of each
;      pixel.
;
; INPUTS:
;      DECOMP    - structure produced by shapelets_decomp.pro
;
; OPTIONAL INPUTS:
;      PSF       - A PSF as a decomp structure type. The model is (re-)convolved
;                  with this PSF in shapelet space before it is pixellated. 
;      X1, X2    - Array of pixel positions, which override any specified in the
;                  decomp structure. Used for irregularly-spaced grids.
;      NRANGE    - Integer array [n_low,n_high]. Ignore coefficients with n 
;                  outsdide this range.
;      TOP       - Integer. Use only this number of (Cartesian) shapelet 
;                  coefficients during recomposition, selected as the ones with 
;                  the largest absolute values.
;      BOTTOM    - Integer. Use only this number of (Cartesian) shapelet 
;                  coefficients during recomposition, selected as the ones with 
;                  the smallest absolute values.
;
; KEYWORD PARAMETERS:
;      /NOOVER   - If set, do not oversample the basis functions.
;      /COMPLEX  - If set, return a complex array (complex part is numerical
;                  error for a Cartesian shapelet model, but can be populated
;                  with polar shapelets).
;      /SKY      - If set, include fit to sky background in reconstructed image.
;      /MEMORY   - Slightly slower but more memory-efficient algorithm for large
;                  image arrays or very high n_max objects.
;
; OUTPUTS:
;      RECOMP    - Reconstructed (2D floating point) image array.
;
; TO DO:
;      Could simplify sky replacement etc. by using shapelets_make_ls_matrix.pro
;
; MODIFICATION HISTORY:
;      Jul 10 - Exponential shapelets option and flexible xarrays added by RM.
;      Jan 09 - Backward compatability of elliptical shapelets improved by RM.
;      Jul 07 - Fixed to work with older versions of IDL by RM.
;      Apr 07 - Elliptical basis functions treated by RM.
;      Apr 05 - COMPLEX keyword added by RM.
;      Apr 04 - PSF reconvolution added by RM.
;      Nov 01 - Numerical integration of basis functions added by Richard Massey.
;      Feb 01 - Modified by AR to allow oversampling of the basis functions
;      Jul 99 - Written by Alexandre Refregier

View the full source code for this routine, return to the shapelets web page, or return to the code help menu.