ct_snr vers3.4
03-27-01 MJF

	Evaluation of the signal to noise reconstruction in 
	a reconstructed image in relation to the SNR of 
	the projection views.	

example:

	ct_snr << EOF
	delta
	mu_eff
	snr
	views
	labelflag
	EOF

standard output:

        The following is returned:

		#voxel size, cm:       5.0000001E-02
		#mu_eff, cm-1:          5.000000    
		#number of views:             800
		#SNR of the CT image:   2000.000    
		  2000.000    

	The returned result for SNR is the mu_eff value  divided by
	the estimate of the noise in a reconstructed image.
	Within the comment lines the parameters input to the routine
	are recorded along with the result.
	For use in a script, a flag of 0 will just return the result
	with no comment information.

directories/links: none

arguments:

	delta:  3D voxel size in cm
	mu_eff: effective attenuation coef., cm-1
	snr:    signal to noise ratio of the projection
	        view in linear signal space.
	views:  number of views being reconstructed
	flag:   flag=1 reports parameters, 0 to suppress comment lines

associated files: none

method:	
	Computationally this is extremely simple code.
	The input parameters are simply used  to compute the  result
	using the following equation;

	SNR_ct = mu_eff * ((2.0**(1.5))*delta*(views**.5))*snr

	This result is derived analytically for the reconstruction
	of an object using parallel ray projections.
	It is a very good approximation for fan beam and cone
	beam projections. The constants in the equation result specifically
	from a reconstruction filter which is a sinc function extending
	to the limiting frequency.  No account is otherwise taken of
	noise correlation in the projections. 

	The input snr is that of the linear data for the projection view. 
	This is related to the noise equivalent quanta, Q, for the
	detected radiation beam passing through the center of the object.
	(i.e. snr = sqrt(Q)). Projection views are often transformed from
	linear raw signal to to a value proportional to the log 
	of the signal. The noise of the projection in log space is
	proportional to the relative noise, NSR, of the projection in
	linear space.

	You will notice in this equation that mu_eff appears with linear
        proportionality. The units of mu_eff (cm-1) cancel the units of
	delta (cm-1) so that the resulting SNR is nondimensional.