obir

Osher’s Bregman-iterated regularization method

Syntax

P = obir(S,K,r,'type',alpha)
P = obir(___,'Property',Value)
Parameters
  • S - Input signal (N-element array)
  • K - Dipolar kernel (NxM-element array)
  • r - Distance Axis (N-element array)
  • type - Regularization type (string)
  • alpha - Regularization parameter (scalar)
Returns
  • P - Distance Distribution (M-element array)

Description

P = obir(S,K,r,'type',alpha)

Fit a distance distribution P on a distance axis r to the signal S according to the kernel K. The (M-2)xM point regularization matrix L and regularization parameter alpha control the regularization properties.

The type of regularization employed in obir is set by the 'type' input argument. The regularization models implemented in obir are:

  • 'tikhonov' - Tikhonov regularization
  • 'tv' - Total variation regularization
  • 'huber' - Pseudo-Huber regularization

Additional Settings

Additional settings can be specified via name-value pairs. All property names are case insensitive and the property-value pairs can be passed in any order after the required input arguments have been passed.

P = obir(___,'Property1',Value1,'Property2',Value2,___)
  • 'NoiseLevelAim' - Noise level aim value

    Level (standard deviation) of noise at which Bregman iterations must stop. If not specified the noise is automatically computed using the noiselevel function.

    Default: [empty]

    Example:

    P = obir(___,'NoiseLevelAim',0.05)
  • 'RegOrder' - Regularization matrix order

    Order of the regularization operator.

    Default: 2

    Example:

    P = obir(___,'RegOrder',3)
  • 'DivergenceStop' - Stop if divergence of residual value

    Specify whether the Bregman iterations must be stopped if the functional value increases instead of decreasing.

    Default: false

    Example:

    P = obir(___,'DivergenceStop',true)
  • 'MaxOuterIter' - Maximal number of Bregman iterations

    Maximal number of allowed Bregman iterations specified as a scalar value.

    Default: 5000

    Example:

    P = obir(___,'MaxOuterIter',1e5)
  • 'AxisHandle' - Axis handle to plot intermediate results

    Axis handle for plotting. If specified the state of the distance distribution at each Bregman iteration is displayed on the given axis object.

    Default: [empty]

    Example:

    P = obir(___,'AxisHandle',gca)
  • 'Solver' - Optimization solver

    Numerical solver employed for the minimization of the regularization functional models.

    • 'fnnls' - Fast non-negative least squares solver
    • fmincon - Constrained non-linear minimization solver

    Default: 'fnnls'

    Example:

    P = obir(___,'Solver','fmincon')
  • 'TolFun' - Optimizer tolerance value

    Optimizer function tolerance. The solver stops once the regularization functional evaluation reaches a value lower than this tolerance. Lower values increase the precision of the result, albeit at the cost of longer computation times.

    Default: 1e-9

    Example:

    P = obir(___,'TolFun',1e-20)
  • 'MaxIter' - Maximal solver iterations

    Maximum number of iterations of the solver. After the solver exceeds this number the optimization will stop. This option is only relevant for the 'fmincon' solver.

    Default: 2e7

    Example:

    P = obir(___,'MaxIter',1e10)
  • 'MaxFunEval' - Maximal solver function evaluations

    Maximum number of function evaluation of the solver. After the solver exceeds this number the optimization will stop. This option is only relevant for the 'fmincon' solver.

    Default: 2e7

    Example:

    P = obir(___,'MaxFunEval',1e10)