Preprocessing for Selavy

A summary of the different types of preprocessing available to Selavy. This refers to work done on the image prior to source-finding, to enhance the detectability of objects. Some of these algorithms are from the Duchamp source-finder, and are described in the Duchamp User’s Guide and Whiting (2012), MNRAS 421, 3242.

Ó? trous wavelet reconstruction

Algorithm details

One way Selavy can try to increase the apparent signal-to-noise of objects is to perform a thresholded multi-resolution wavelet reconstruction of the data, using the Óš trous algorithm. Briefly, the algorithm smoothes the data with progressively larger kernels (doubling the separation of the kernel elements each time), then forms wavelet arrays from the difference of successive smoothed arrays. These wavelet arrays describe the amount of signal at that scale at that location. Applying a threshold to these, and only keeping signal above the threshold, can reject a lot of the random noise present in the image. Once thresholded, the wavelet arrays are summed back together, then source extraction can be performed, generally to a quite low level. Wavelet reconstruction tends to give very good reliability.

The key parameters controlling the reconstruction are the dimensionality of the reconstruction, the level of the thresholding applied to the wavelet arrays, and the range of scales to make use of. There are other, more minor, parameters governing the specifics of the kernel, and the criterion for determining when to stop the reconstruction (looking at the degree of convergence, testing if there is still significant signal being missed).

Reconstruction parameters

Note that these are not in the usual hierarchical format (constrast with the 2D1D case below) – this is because this algorithm originates with the Duchamp source finder, which has a flat parameter set input.

Parameter	Type	Default	Explanation
flagAtrous	bool	false	Whether to use the wavelet reconstruction
reconDim	int	1	The number of dimensions in which to perform the reconstruction. 1 means reconstruct each spectrum separately, 2 means each channel map is done separately, and 3 means do the whole cube in one go.
snrRecon	float	4	Signal-to-noise threshold applied to wavelet arrays – only wavelet coefficients at least this many sigma above the mean are included in the reconstruction.
scaleMin	int	1	Minimum wavelet scale to include in reconstruction. A value of 1 means ò??use all scalesò??.
scaleMax	int	0	Maximum wavelet scale to use in the reconstruction. If 0 or negative, then maximum scale is calculated from the size of the array.
filterCode	int	1	Code number for the filter that defines the smoothing kernel. Consult the User Guide for details.
reconConvergence	float	0.005	The criterion for convergence of the reconstruction - the relative changes in the standard devidation of the residuals must be less than this.

Smoothing

Alternatively, the array can be smoothed by a filter of a single scale. This can be done either in the spatial domain or the spectral domain. If spatial, a two-dimensional Gaussian kernel is used. If spectral, a hanning-style filter of a defined width is used. Smoothing can provide catalogues with very good completeness, depending on the appropriateness of the filter.

Parameter	Type	Default	Explanation
flagSmooth	bool	false	Whether to smooth the data prior to searching.
smoothType	string	spectral	The smoothing method used: either “spectral” or “spatial”
hanningWidth	int	5	The width of the Hanning spectral smoothing kernel
kernMaj	float	3	The FWHM of the major axis of the 2D Gaussian smoothing kernel, in pixels.
kernMin	float	3	The FWHM of the minor axis of the Gaussian kernel, in pixels
kernPA	float	0	The position angle, in degrees, of the Gaussian kernel
smoothEdgeMethod	string	equal	The method for dealing with the pixels on the edge of the image when doing the spatial smoothing. Can be one of: equal (all pixels treated the same), truncated (pixels near edge blanked out) or scale (pixels near edge scaled by the relative amount of the smoothing kernel used).
spatialSmoothCutoff	float	1.e-10	The value of the Gaussian kernel defining the width of the 2D kernel array. Relative to the peak of 1.

2D1D Wavelet reconstruction

Selavy also provides the ability to reconstruct the image using the 2D1D wavelet transform (see FlÓÆer & Winkel 2012, PASA 29, 244). This operates as an alternative reconstruction method to the Duchamp Óš trous algorithm, and works with the rest of the source finding in exactly the same way. The parameter-set interface is different, however, to better use the capabilities of the parameter set - see below.

Algorithm details

The version of the algorithm being used is a specially-constructed version provided by Lars FlÓÆer, that has the same interface as the Duchamp wavelet algorithms. The parameters that are available to the user are similar to those required by the Óš trous algorithms. The key one is the reconstruction threshold snrRecon, that defines the n-sigma threshold used in keeping or rejecting wavelet coefficients. The minimum and maximum scales to be considered for the spatial and spectral directions can be specified (the defaults use all possible scales). The maximum number of iterations can be specified also (unlike the Duchamp algorithms, no convergence test is applied) - on subsequent iterations, the residual (input - output) is searched for further signal not yet recovered in the output array. There is also the option not in the Duchamp algorithms to enforce “positivity” in the final result - essentially setting negative values to zero.

2D1D parameters

Parameter	Type	Default	Explanation
recon2D1D	bool	false	Whether to use the 2D1D algorithm
recon2D1D.snrRecon	float	3.0	The signal-to-noise threshold applied to the wavelet coefficients
recon2D1D.useDuchampStats	bool	false	Whether to find the stats in the same way as the Duchamp algorithms.If false, the rms of the wavelet array is used in combination with snrRecon
recon2D1D.minXYscale	int	1	The minimum spatial scale to be considered in the reconstruction
recon2D1D.maxXYscale	int	-1	The maximum spatial scale to be considered in the reconstruction. If negative, the maximum possible is used - ln_2(min(xdim,ydim))
recon2D1D.minZscale	int	1	The minimum spectral scale to be considered in the reconstruction
recon2D1D.maxZscale	int	-1	The maximum spectral scale to be considered in the reconstruction. If negative, the maximum possible is used - ln_2(zdim)
recon2D1D.enforcePositivity	bool	true	Whether to set negative values in the output result to zero.
recon2D1D.maxIter	int	1	The maximum number of iterations of the algorithm