Deconvolution Methods in ZEN

Nearest Neighbor

K. Castleman, “Digital image processing”, Prentice Hall 1997

Algorithm (default):

Nearest Neighbor

Ad-hoc “2D de-blurring algorithm” focuses on subtraction of out of focus blur.

Regularized Inverse

also known as:

Linear Least Squares

For zero order g-difference:

Schaefer et al. (2001)

Algorithm (default):

Regularized Inverse Filter

Advanced settings > Regularization:

Zero order

Uses difference of observation and estimate as regularization term.

Regularized Inverse

also known as:

Linear Least Squares

For first order regularization, or Good’s roughness:

Verveer et al. (1997)

Algorithm:

Regularized Inverse

Advanced settings > Regularization:

First order

Uses Good’s roughness first derivative of estimate as regularization term.

Regularized Inverse

also known as:

Linear Least Squares

In conjunction with structured illumination microscopy (ApoTome)

Schaefer et al. (2006)

Schaefer et al. (tbs)

Algorithm:

Regularized Inverse

Advanced settings > Regularization:

Zero/First order

Patented method for maximum exploitation of ApoTome raw images.

Fast Iterative

Also known as:

Meinel Algorithm

Gold Meinel

Meinel (1986)

Algorithm (default):

Fast Iterative

Advanced settings > Likelihood:

Poisson (Meinel)

Classic, non-regularized Meinel algorithm.

Fast Iterative

Meinel Algorithm + Regularization:

Meinel (1986),

For zero order g-difference:

Schaefer et al. (2001)

Algorithm:

Fast Iterative

Advanced settings:

- Likelihood:

Poisson (Meinel)

- Regularization:

Zero order

Regularized Meinel algorithm using g-difference (difference of observation and estimate) term.

Fast Iterative

Meinel Algorithm +
Optimization

Meinel (1986),

Biggs (1998)

Algorithm:

Fast Iterative

Advanced settings:

- Likelihood:

Poisson (Meinel)

- Regularization:

None/Zero order

- Optimization:

Numerical Gradient

Meinel algorithm using a numerical gradient estimator as proposed by D. Biggs.

Fast Iterative

Also known as:

Richardson Lucy (RL) Algorithm

Richardson (1972)

Lucy (1974)

Algorithm:

Fast Iterative

Advanced settings > Likelihood:

Poisson (Richardson, Lucy)

Classic, original non-regularized Richardson Lucy algorithm. May need many more iterations than any other algorithm.

Fast Iterative

Also known as:

Richardson Lucy Algorithm +
Optimization

Richardson (1972)

Lucy (1974)

Biggs (1998)

Algorithm:

Fast Iterative

Advanced settings:

- Likelihood:

Poisson (Richardson, Lucy)

- Optimization:

Numerical Gradient

Classic, original non-regularized Richardson Lucy algorithm. Improved rate of convergence. About a factor of 10 faster than RL using a numerical gradient estimator as proposed by D. Biggs.

Constrained Iterative

Verveer et al. (1997)

Schaefer et al. (2001)

Algorithm (default):

Constrained Iterative

Advanced settings:

- Likelihood:

Poisson

- Regularization:

Zero order

Generic conjugate gradient restoration using squared estimate to impose positivity. Uses difference of observation and estimate as regularization term.

Constrained Iterative

Verveer et al. (1997)

Schaefer et al. (2001)

Algorithm:

Constrained Iterative

Advanced settings:

- Likelihood:

Poisson

- Regularization:

First order

Generic conjugate gradient restoration using squared estimate to impose positivity. Uses Good’s roughness derivative operator as regularization term.

Constrained Iterative

Tikhonov (1977)

Verveer et al. (1997)

Schaefer et al. (2001)

Algorithm:

Constrained Iterative

Advanced settings:

- Likelihood:

Poisson

- Regularization:

Second order

Generic conjugate gradient restoration using squared estimate to impose positivity. Uses Tikhonov Miller Phillips second derivative operator as regularization term.

Constrained Iterative

Verveer et al. (1997)

Schaefer et al. (2001)

Algorithm:

Constrained Iterative

Advanced settings:

- Likelihood:

Gauss

- Regularization:

Zero order

Generic conjugate gradient restoration using squared estimate to impose positivity. Uses difference of observation and estimate as regularization term.

Constrained Iterative

Verveer et al. (1997)

Schaefer et al. (2001)

Algorithm:

Constrained Iterative

Advanced settings:

- Likelihood:

Gauss

- Regularization:

First order

Generic conjugate gradient restoration using squared estimate to impose positivity. Uses Good’s roughness derivative operator as regularization term.

Constrained Iterative

Also known as: ICTM

Iterative Constrained Tikhonov Miller

van der Voort et al. (1995) Verveer et al. (1997)

Schaefer et al. (2001)

Algorithm:

Constrained Iterative

Advanced settings:

- Likelihood:

Gauss

- Regularization:

Second order

Generic conjugate gradient restoration using squared estimate to impose positivity. Uses Tikhonov Miller Phillips second derivative operator as regularization term.

Constrained Iterative

Verveer et al. (1997)

Schaefer et al. (2001)

Algorithm:

Constrained Iterative

Advanced settings:

- Likelihood:

Poisson/Gauss

- Regularization:

0/1/2nd order

- Optimization:

Line search/Analytical

Generic conjugate gradient restoration using squared estimate to impose positivity.

Default for optimization is the fast analytical (Newton Raphson) method. Line search may be more accurate but is also much slower.