Introduction

A wavelet package concerning two dimensional imaging has been implemented in MIDAS. This package contains several wavelet transform algorithms, specific tools for the wavelet transform, visualisation commands, and three applications of the use of the wavelet transform: filtering, comparison, and deconvolution. These commands can be called if the wavelet context has been initialized by:

set/context wavelet

Table 14.1 shows the available commands.

 

Table 14.1: Midas commands

Commands	Description
TRANSF/WAVE	Image Wavelet [Algo] [Nbr_Scale] [Fc]
	creates the wavelet transform of an image
RECONS/WAVE	Wavelet Rec_Image
	reconstructs an image from its wavelet transform
HEADER/WAVE	Wavelet
	gives information about a wavelet transform
INFO/WAVE	Wavelet
	gives information about each scale of a wavelet transform
EXTRAC/WAVE	Wavelet Image_Out Scale_Number
	creates an image from a scale of the wavelet transform
ENTER/WAVE	Wavelet_in Image_in Scale_Number Wavelet_out
	replaces a scale of a wavelet transform by an image
VISUAL/WAVE	Wavelet [Visu_Type]
	visualizes a wavelet transform with default parameters
VISUAL/CUBE	Wavelet [output_file] [Disp] [Visu_Mode] [Display]
	visualizes a wavelet transform in a cube
VISUAL/CONT	Wavelet [Graphic_Number] [Visu_Mode] [Contour_Level]
	visualizes the contours of a wavelet transform
VISUAL/SYNT	Wavelet [output_file] [Display_Number] [Display]
	creates a visualization image from a wavelet transform
VISUAL/PLAN	Wavelet [Display]
	display each scale of the wavelet transform in a window
VISUAL/PERS	Wavelet [out_file] [Disp_N] [Visu_Mode] [Incr] [Thres] [Display]
	visualizes in perpsective a wavelet transform
FILTER/WAVE	I_In I_Out [Algo] [T_Filter] [Iter_Nbr] [N_Scale] [N_Sigma] [Noise]
	filters an image by using the wavelet transform
COMPAR/WAVE	Imag_1 Imag_2 [N_Scal] [N_Sigma] [T_Cor] [T_Snr] [Disp] [Init]
	compares two images in the wavelet space
PLOT/SNR	Tab_Snr
	plots the SNR table resulting from the comparison
PLOT/COR	Tab_Correl
	plots the correlation resulting from the comparison
TUTORIAL/WAVE	visualizes the wavelet transform of the galaxy NGC2997
	with several algorithms
DIRECT/WAVE	Imag_In Psf Imag_Out [Nb_Scales] [$\gamma_1$,$\gamma_2$,$\gamma_3$,...]
	deconvolution with a multiresolution Tichonov's Regularisation
CITTERT/WAVE	Im_In Psf Im_Out [Resi] [Scal, Iter] [N_Sig, Noise] [Eps] [Fwhm]
	deconvolution by the regularized Van Cittert's algorithm
GRAD/WAVE	Im_In Psf Im_Out [Resi] [Nb_Scales] [N_Sigma, Noise] [Eps] [Max_Iter]
	deconvolution by the regularized one-step gradient algorithm
LUCY/WAVE	Im_In Psf Im_Out [Resi] [Nb_Scales] [N_Sigma, Noise] [Eps] [Max_Iter]
	deconvolution by the regularized Lucy's algorithm
TRAN1D/WAVE	Im_In Wave_Out [Num_Trans] [Num_Line] [Channel] [Nu]
	one dimensional wavelet transform
REC1D/WAVE	Wave_in Im_out [Num_Trans] [Channel] [Nu0]
	reconstructs a 1D signal from its wavelet transform