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Report for folder /home/ancmt/matlab_octave/SynapseToolBox/wavelets/PURE-LET-Denoise/purelet_tbx

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batch_purelet_denoise
Framewise PURE-LET denoising for 3D data `x'. 
  Framewise PURE-LET denoising for 3D data `x'. 
  
  This function is a wrapper that calls purelet_denoise iteratively for each 2D
  subarray of the 3D array `x' (data is sliced along the third dimension)
  
  SYNTAX:
  
  [y,alphas,sigmas,deltas]=batch_purelet_denoise(x)
  [y,alphas,sigmas,deltas]=batch_purelet_denoise(x,doPar)
  [y,alphas,sigmas,deltas]=batch_purelet_denoise(x,doPar,bkgCoords)
  
  MANDATORY INPUTS:
  
  x     : three dimensional grid data (array) e.g. a stack of 2D images (frames)
  
  OPTIONAL INPUTS:
  
  doPar     : scalar boolean, or empty matrix; when true, uses matlab parallel
              processing toolbox for concurrent processing of each frame; else,
              frames are processed in sequence; default is true if parallel
              computing toolbox is installed, false otherwise
  
  bkgCoords : cell array with two elements, or empty matrix; defines a
              rectangular area for the calculation of noise parameters (gain,
              offset, variance)
  
              Its elements are index arrays respectively into the first and
              second dimension for each frame in `x' representing the data
              subset for which noise parameters are calculated; whenever 
              an element is the empty matrix, the whole extent of the
              corresponding dimension will be used
  
              Example 1: 
  
              {1:50, 200:256} : defines the same rectangle which could be obtained
              from the kth frame of x by calling directly x(1:50, 200:256,  k)
  
              Example 2: 
  
              {[], 200:256} : defines the same rectangle which could be obtained
              from the kth frame of x by calling directly x(:, 200:256,  k)
  
              Example 3: 
  
              {1:50, []} : defines the same rectangle which could be obtained
              from the kth frame of x by calling directly x(1:50, :,  k)
  
              Example 4: 
  
              {[], []} = defines the same rectangle which could be obtained
              from the kth frame of x by calling directly x(:, :,  k) - i.e.,
              the entire kth frame of x.
  
              Note that {[],[]} and {[]} are interpreted as representing the same
              thing, i.e, the entire frame data.
  
  useWTvar  : scalar boolean, default false; switch between AWGN variance
              estimators: when true, use Donoho's robust AWGN variance estimator
              in `wt_variance' routine; else, use the value returned from the
              block processing routine `pawgn_noise_est'  
  
  OUTPUTS:
  
  y         : de-noised version of x
  
  alphas,sigmas,deltas: AWGN parameters estimated for each frame of x
  
  See also purelet_denoise, purelet_theta, pawgn_noise_est, wt_variance
  
  References:
  
  Luisier, F., T. Blu, and M. Unser. 2011. Image denoising in mixed
  Poisson-Gaussian noise. IEEE Trans. Image Process. 20:696?708.
  
  C. M. Tigaret, K. Tsaneva-Atanasova, G. L. Collingridge, and J. R. Mellor.
  Wavelet transform-based de-noising for two-photon imaging of synaptic Ca2+
  transients. Biophysical Journal, 104(5):1006 ? 1017, 2013. 
  
  Copyright 2011-2013 by Cezar M. Tigaret <Cezar.Tigaret@bristol.ac.uk>

No example
69: See also purelet_denoise, purelet_theta, pawgn_noise_est, wt_variance
80: % Copyright 2011-2013 by Cezar M. Tigaret 
pawgn_noise_est
Estimate gain, offset and variance in image data with mixed Poisson-AWGN noise
  Estimate gain, offset and variance in image data with mixed Poisson-AWGN noise
  
  SYNTAX:
  
  [alpha, sigma2, delta]=pawgn_noise_est(x)
  
  [alpha, sigma2, delta]=pawgn_noise_est(x, blkSize)
  
  MANDATORY INPUT:
  
  x       : vector or matrix data (double precision)
  
  OPTIONAL INPUT:
  
  blkSize : scalar, integer (default 8)
  
  OUTPUTS:
  
  alpha   : the gain
  
  sigma2  : variance
  
  delta   : offset
  
  See also batch_purelet_denoise, purelet_denoise, purelet_theta
  
  References:
  
  
  Luisier, F., T. Blu, and M. Unser. 2011. Image denoising in mixed
  Poisson-Gaussian noise. IEEE Trans. Image Process. 20:696?708.
  
  Boulanger, J., et al. 2010. Patch-based nonlocal functional for denoising
  fluorescence microscopy image sequences. IEEE Trans. Med. Imag. 29:442?454.
  
  Copyright 2011-2013 by Cezar M. Tigaret <Cezar.Tigaret@bristol.ac.uk>
  

No example
27: See also batch_purelet_denoise, purelet_denoise, purelet_theta
38: % Copyright 2011-2013 by Cezar M. Tigaret 
purelet_denoise
PURE-LET de-noising for 2D data `x'
  PURE-LET de-noising for 2D data `x'
  
  SYNTAX:
  
  xhat = purelet_denoise(x, sigma2)
  xhat = purelet_denoise(x, sigma2, showProgress)
  xhat = purelet_denoise(x, sigma2, showProgress, doTimer)
  
  MANDATORY INPUTS:
  
  x      : two dimensional array (noisy data), double precision
  
  sigma2 : estimated AWGN variance; scalar, double precision, or empty matrix;
           when empty, the sigma2 is estimated from the detail coefficients of
           the first level of wavelet transform (Donoho, 1993)
  
  OPTIONAL INPUTS:
  
  showProgress : scalar, boolean, or empty; default is true - show a progressbar
  
  doTimer      : scalar, boolean, or empty; default is true - show elapsed
                 processing time
  
  OUTPUT
  
  xhat    - denoised version of `x'
  
  See also batch_purelet_denoise, purelet_theta, pawgn_noise_est, wt_variance
  
  References:
  
  Luisier, F., T. Blu, and M. Unser. 2011. Image denoising in mixed
  Poisson-Gaussian noise. IEEE Trans. Image Process. 20:696?708.
  
  Donoho, D. L. 1993. Nonlinear wavelet methods for recovery of signals,
  densities, and spectra from indirect and noisy data. In Proceedings of
  Symposia in Applied Mathematics. American Mathematical Society, Providence,
  RI. 173?205.
  
  Copyright 2011-2013 by Cezar M. Tigaret <Cezar.Tigaret@bristol.ac.uk>

No example
30: See also batch_purelet_denoise, purelet_theta, pawgn_noise_est, wt_variance
42: % Copyright 2011-2013 by Cezar M. Tigaret 
purelet_theta
SYNTAX:
  SYNTAX:
 
             [t, dt_dx, dt_dy, dt_dxdy, dt2_dx2, dt2_dy2]=...
              purelet_theta(x,y,v,b,r,p,k,debugOn)
 
  INPUTS:
  x, y       = wavelet and scaling (or GDC) coefficients, respectively
  v          = variance of AWGN
  b          = scale-dependent factor (2^(-j/2))
  r,p,k      + theta function parameters (see Luisier et al 2011)
  
  implements
 
  t1 = x
              _               _
             |     _      _ p  |
             |    |    x   |   |
             |  - |--------|   |
             |    | r*t(w) |   |
             |    |_      _|   |
             |_               _|
  t2 = x * e
 
  where t(w) = sqrt(b * w + v), 
 
  with w = y*tanh(k*y), k=100, a differentiable approximation of abs(y)
    
  and typically with r = 3 and p = 8
    
  the corresponding derivatives of the theta functions will be taken with
  respect to w (which aproximates |y|) and NOT to y itself !!!
 
  
  because the image data is a function that can take only positve integer
  numbers, imposing unity as a lower bound for denominators when calculating
  the derivatives does not bring a great loss of generality, while avoiding
  unstable results (i.e., NaNs) especially for very low intensity signals
    
  Reference:
  
  Luisier, F., T. Blu, and M. Unser. 2011. Image denoising in mixed
  Poisson-Gaussian noise. IEEE Trans. Image Process. 20:696?708.
  
  Copyright 2011-2013 by Cezar M. Tigaret <Cezar.Tigaret@bristol.ac.uk>

No example
No see-also line
47: % Copyright 2011-2013 by Cezar M. Tigaret 
wt_variance
Estimates AWGN variance in `x' from the median absolute deviation of the
  Estimates AWGN variance in `x' from the median absolute deviation of the
  wavelet coefficients at highest resolution (Haar domain), according to the
  formula in :
  Donoho, D. L. 1993. Nonlinear wavelet methods for recovery of signals,
  densities, and spectra from indirect and noisy data. In Proceedings of
  Symposia in Applied Mathematics. American Mathematical Society, Providence,
  RI. 173?205. 
  
  SYNTAX:
  
  y = wt_variance(x)
  
  INPUT:
  
  x  : matrix data
  
  OUTPUT:
  
  y  : estimated variance
  
  Copyright 2011-2013 by Cezar M. Tigaret <Cezar.Tigaret@bristol.ac.uk>
  

No example
No see-also line
23: % Copyright 2011-2013 by Cezar M. Tigaret