Deconvolution _Process_Console_parameters?

[Herbert_W]

Hi,

Could anyone explain the parametes in this list (row)
Sigma, DeltaSigma, Sigma(s?), n

and what is the meaning of the de(in)creasing  numbers (column):






Thank you
Herbert, Austria

[Juan Conejero]

Hi Herbert,

These data are provided for regularized deconvolution algorithms (Richardson-Lucy and Van Cittert). At teach iteration, the following data are provided for the residual image. The residual is the difference between the original image and the current deconvolved image (which is the image resulting from the previous iteration):

sigma
Standard deviation.

Delta_sigma
This is the quotient:

(sigma₀ - sigma)/sigma

where sigma₀ is the standard deviation of the previous residual (or the value of sigma in the previous iteration).

sigma_s
This is an estimate of the standard deviation of the noise in the residual image.

n
The fraction of significant structures in the [0,1] range, where 1 corresponds to the number of pixels in the image. At each iteration, regularized algorithms divide the image into noise and significant structures. Significant structures are preserved in the solution and the noise is removed or attenuated.

These data can be used to know how the algorithms converge. Regularized algorithms are designed to converge to a solution where the deconvolved image cannot be further improved. If the algorithm converges, the sigma and Delta_sigma values decrease at each iteration. The noise (sigma_s) and the fraction of significant data (n) should stabilize after a sufficiently large number of iterations. With too many iterations the algorithms may start to diverge, which you can detect as negative Delta_sigma values. Sometimes this happens after a relatively short number of iterations. Sometimes the algorithms start converging after a short period of divergence.

[Herbert_W]

Hi Juan,

Thank you very much indeed for your effort to reply all questions.

Herbert, Austria