fitmultimodel

Automatic multi-component parametric model fitting of a distance distribution

Syntax

P = fitmultimodel(S,K,r,@dd_model,Nmax)
P = fitmultimodel(S,t,r,@dd_model,Nmax)
P = fitmultimodel(S,K,r,@dd_model,Nmax,metric)
P = fitmultimodel(S,t,r,@dd_model,Nmax,metric,'Background',bg_model)
P = fitmultimodel({V1,V2,___},{K1,K2,___},r,@dd_model,Nmax,metric)
P = fitmultimodel({V1,V2,___},{t1,t2,___},r,@dd_model,Nmax,metric)
P = fitmultimodel({V1,V2,___},{t1,t2,___},r,@dd_model,Nmax,metric,'Background',bg_model)
P = fitmultimodel(___,'Property',Value)
[P,param,Pci,paramci,Nopt,metrics,Peval] = fitmultimodel(___)
Parameters
  • S - Input signal (N-element array)
  • K - Dipolar kernel (NxM-element array)
  • r - Distance Axis (N-element array)
  • t - Time Axis (N-element array)
  • @dd_model - Parametric model basis function (function handle)
  • Nmax - Maximum number of components (scalar)
  • metric - Metric for model selection (string)
Returns
  • P - Fitted distance distribution (M-element array)
  • param - Fitted model parameters (W-array)
  • Pci - Fitted distribution confidence intervals (Mx2-array)
  • paramci - Fitted parameters confidence intervals (Wx2-array)
  • Nopt - Optimal number of components (scalar)
  • metrics - Evaluated model selection functionals (cell array)
  • Peval - Fitted distance distributions for each multi-component model (Nmax x N matrix)

Description

P = fitmultimodel(S,K,r,@dd_model,Nmax)

Fits the dipolar signal S to a distance distribution P using a multi-component parametric model according to the dipolar kernel K and distance axis r. The multi-component model is constructed from the basis function provided as @dd_model. The function chooses the optimal number of components distributions up to a maximum number given by Nmax by means of the corrected Akaike information criterion (AICC).

P = fitmultimodel(S,K,r,@,dd_model,Nmax,metric)

The metric employed for the selection of the optimal number of components can be specified as an additional input metric. The accepted inputs are:

  • 'aic' - Akaike information criterion
  • 'aicc' - Corrected Akaike information criterion
  • 'bic' - Bayesian information criterion
P = fitmultimodel(S,t,r,@,dd_model,Nmax)

If the default kernel is to be used, the time-axis can be passed instead of the kernel.

P = fitmultimodel(S,t,r,@dd_model,Nmax,metric,'Background',model)

By passing the 'Background' option, the background function and modulation depth are fitted along the multi-component distribution parameters.

P = fitmultimodel({V1,V2,___},{K1,K2,___},r,@dd_model,Nmax,metric)

Passing multiple signals/kernels enables distance-domain global fitting of the parametric model to a single distribution. The global fit weights are automatically computed according to their contribution to ill-posedness. The multiple signals are passed as a cell array of arrays of sizes N1, N2,… and a cell array of kernel matrices with sizes N1xM, N2xM, … must be passed as well.

P = fitmultimodel({V1,V2,___},{t1,t2,___},r,@dd_model,Nmax,metric)
P = fitmultimodel({V1,V2,___},{t1,t2,___},r,@dd_model,Nmax,metric,'Background',model)

Similarly, time-domain global fitting can be used when passing time-domain models and the model time axes {t1,t2,___} of the corresponding signals. If a background model is specified, it will be applied to all input signals.

[P,param,Nopt,metrics] = fitmultimodel(____)

If requested alongside the distribution P, the optimal fit model parameters param, as well their respective confidence intervals Pci and paramci the optimal number of components Nopt and evaluated selection metrics metrics are returned.

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 = fitmultimodel(___,'Property1',Value1,'Property2',Value2,___)
  • 'Background' - Parametric background model

    Function handle of the corresponding time-domain background model.

    Default: [empty] - Background and modulation depth are not fitted

    Example:

    P = fitmultimodel(___,'Background',@bg_hom3d)
  • 'Upper' - Parameters upper bound constraints

    An array of W-elements containing the upper bounds for the W parameters accepted by the model function @dd_model.

    Default: [empty] - Uses the model’s default upper bound values

    Example:

    P = fitmultimodel(___,@dd_gauss,___,'Upper',[rmean_max FWHM_max])
  • 'Lower' - Parameters lower bound constraints

    An array of W-elements containing the lower bounds for the W parameters accepted by the model function @dd_model.

    Default: [empty] - Uses the model’s default lower bound values

    Example:

    P = fitmultimodel(___,@dd_gauss,___,'Upper',[rmean_in FWHM_min])

  • See fitparamodel for a detailed list of other property-value pairs accepted by the function.