Пример #1
0
def test_lorentzian():
    """
    Test the lorentzian function
    """
    freq = np.linspace(0,6,100)
    freq0 = 3
    area = 1
    hwhm = 1
    phase = np.pi
    baseline0 = 1
    baseline1 = 0
    ut.lorentzian(freq, freq0, area, hwhm, phase, baseline0, baseline1)
Пример #2
0
def fit_lorentzian(spectra, f_ppm, lb=2.6, ub=3.6):
    """
   Fit a lorentzian function to spectra

   This is used in estimation of the water peak and for estimation of the NAA
   peak.  
   
   Parameters
   ----------
   spectra : array of shape (n_transients, n_points)
      Typically the sum of the on/off spectra in each transient.

   f_ppm : array

   lb, ub: floats
      In ppm, the range over which optimization is bounded
   
   """
    # We are only going to look at the interval between lb and ub
    idx = ut.make_idx(f_ppm, lb, ub)
    n_points = np.abs(idx.stop - idx.start)
    n_params = 6
    # Set the bounds for the optimization
    bounds = [
        (lb, ub),  #peak
        (0, None),  #area
        (0, None),  #hwhm
        (-np.pi / 2, np.pi / 2),  #phase
        (None, None),  #offset
        (None, None)
    ]  #drift

    model = np.empty((spectra.shape[0], n_points))
    signal = np.empty((spectra.shape[0], n_points))
    params = np.empty((spectra.shape[0], n_params))
    for ii, xx in enumerate(spectra):
        # We fit to the real spectrum:
        signal[ii] = np.real(xx[idx])
        params[ii] = _do_lorentzian_fit(f_ppm[idx],
                                        np.real(signal[ii]),
                                        bounds=bounds)

        model[ii] = ut.lorentzian(f_ppm[idx], *params[ii])

    return model, signal, params
Пример #3
0
def fit_lorentzian(spectra, f_ppm, lb=2.6, ub=3.6):
   """
   Fit a lorentzian function to spectra

   This is used in estimation of the water peak and for estimation of the NAA
   peak.  
   
   Parameters
   ----------
   spectra : array of shape (n_transients, n_points)
      Typically the sum of the on/off spectra in each transient.

   f_ppm : array

   lb, ub: floats
      In ppm, the range over which optimization is bounded
   
   """
   # We are only going to look at the interval between lb and ub
   idx = ut.make_idx(f_ppm, lb, ub)
   n_points = np.abs(idx.stop - idx.start) 
   n_params = 6
   # Set the bounds for the optimization
   bounds = [(lb,ub), #peak
             (0,None), #area
             (0,None), #hwhm
             (-np.pi/2, np.pi/2), #phase
             (None,None), #offset
             (None, None)] #drift

   model = np.empty((spectra.shape[0], n_points))
   signal = np.empty((spectra.shape[0], n_points))
   params = np.empty((spectra.shape[0], n_params))
   for ii, xx in enumerate(spectra):
      # We fit to the real spectrum:
      signal[ii] = np.real(xx[idx])
      params[ii] = _do_lorentzian_fit(f_ppm[idx], np.real(signal[ii]),
                                      bounds=bounds)
      
      model[ii] = ut.lorentzian(f_ppm[idx], *params[ii])
   
   return model, signal, params
Пример #4
0
    def fit_creatine(self, reject_outliers=3.0, fit_lb=2.7, fit_ub=3.5):
        """
        Fit a model to the portion of the summed spectra containing the
        creatine and choline signals.

        Parameters
        ----------
        reject_outliers : float or bool
           If set to a float, this is the z score threshold for rejection (on
           any of the parameters). If set to False, no outlier rejection

        fit_lb, fit_ub : float
           What part of the spectrum (in ppm) contains the creatine peak.
           Default (2.7, 3.5)

        Note
        ----
        We use upper and lower bounds that are a variation on the bounds
        mentioned on the GANNET ISMRM2013 poster [1]_.

        [1] RAE Edden et al (2013). Gannet GABA analysis toolkit. ISMRM
        conference poster.

        """
        # We fit a two-lorentz function to this entire chunk of the spectrum,
        # to catch both choline and creatine
        model, signal, params = ana.fit_two_lorentzian(self.sum_spectra,
                                                       self.f_ppm,
                                                       lb=fit_lb,
                                                       ub=fit_ub)

        # Use an array of ones to index everything but the outliers and nans:
        ii = np.ones(signal.shape[0], dtype=bool)
        # Reject outliers:
        if reject_outliers:
            model, signal, params, ii = self._outlier_rejection(
                params, model, signal, ii)

        # We'll keep around a private attribute to tell us which transients
        # were good (this is for both creatine and choline):
        self._cr_transients = np.where(ii)

        # Now we separate choline and creatine params from each other (remember
        # that they both share offset and drift!):
        self.choline_params = params[:, (0, 2, 4, 6, 8, 9)]
        self.creatine_params = params[:, (1, 3, 5, 7, 8, 9)]

        self.cr_idx = ut.make_idx(self.f_ppm, fit_lb, fit_ub)

        # We'll need to generate the model predictions from these parameters,
        # because what we're holding in 'model' is for both together:
        self.choline_model = np.zeros(
            (self.creatine_params.shape[0],
             np.abs(self.cr_idx.stop - self.cr_idx.start)))

        self.creatine_model = np.zeros(
            (self.choline_params.shape[0],
             np.abs(self.cr_idx.stop - self.cr_idx.start)))

        for idx in range(self.creatine_params.shape[0]):
            self.creatine_model[idx] = ut.lorentzian(
                self.f_ppm[self.cr_idx], *self.creatine_params[idx])
            self.choline_model[idx] = ut.lorentzian(self.f_ppm[self.cr_idx],
                                                    *self.choline_params[idx])
        self.creatine_signal = signal
        self.creatine_auc = self._calc_auc(ut.lorentzian, self.creatine_params,
                                           self.cr_idx)
        self.choline_auc = self._calc_auc(ut.lorentzian, self.choline_params,
                                          self.cr_idx)
Пример #5
0
    def fit_creatine(self, reject_outliers=3.0, fit_lb=2.7, fit_ub=3.5):
        """
        Fit a model to the portion of the summed spectra containing the
        creatine and choline signals.

        Parameters
        ----------
        reject_outliers : float or bool
           If set to a float, this is the z score threshold for rejection (on
           any of the parameters). If set to False, no outlier rejection

        fit_lb, fit_ub : float
           What part of the spectrum (in ppm) contains the creatine peak.
           Default (2.7, 3.5)

        Note
        ----
        We use upper and lower bounds that are a variation on the bounds
        mentioned on the GANNET ISMRM2013 poster [1]_.

        [1] RAE Edden et al (2013). Gannet GABA analysis toolkit. ISMRM
        conference poster.

        """
        # We fit a two-lorentz function to this entire chunk of the spectrum,
        # to catch both choline and creatine
        model, signal, params = ana.fit_two_lorentzian(self.sum_spectra,
                                                       self.f_ppm,
                                                       lb=fit_lb,
                                                       ub=fit_ub)

        # Use an array of ones to index everything but the outliers and nans:
        ii = np.ones(signal.shape[0], dtype=bool)
        # Reject outliers:
        if reject_outliers:
            model, signal, params, ii = self._outlier_rejection(params,
                                                                model,
                                                                signal,
                                                                ii)
            
        # We'll keep around a private attribute to tell us which transients
        # were good (this is for both creatine and choline):
        self._cr_transients = np.where(ii)
        
        # Now we separate choline and creatine params from each other (remember
        # that they both share offset and drift!):
        self.choline_params = params[:, (0,2,4,6,8,9)]
        self.creatine_params = params[:, (1,3,5,7,8,9)]
        
        self.cr_idx = ut.make_idx(self.f_ppm, fit_lb, fit_ub)

        # We'll need to generate the model predictions from these parameters,
        # because what we're holding in 'model' is for both together:
        self.choline_model = np.zeros((self.creatine_params.shape[0],
                                    np.abs(self.cr_idx.stop-self.cr_idx.start)))

        self.creatine_model = np.zeros((self.choline_params.shape[0],
                                    np.abs(self.cr_idx.stop-self.cr_idx.start)))
        
        for idx in range(self.creatine_params.shape[0]):
            self.creatine_model[idx] = ut.lorentzian(self.f_ppm[self.cr_idx],
                                                     *self.creatine_params[idx])
            self.choline_model[idx] = ut.lorentzian(self.f_ppm[self.cr_idx],
                                                    *self.choline_params[idx])
        self.creatine_signal = signal
        self.creatine_auc = self._calc_auc(ut.lorentzian,
                                           self.creatine_params,
                                           self.cr_idx)
        self.choline_auc = self._calc_auc(ut.lorentzian,
                                          self.choline_params,
                                          self.cr_idx)