M-File List
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 |