Deconv_lib

FRC_MultiImg_RL_FFT(dset, max_iter=50, pad=None, epsilon=None, reg=0)[source]

Multi-image Richardson-Lucy deconvolution, performed using FFT. It deconvolves the entire dataset, returning a single deconvoluted image. The PSF is automatically estimated with Fourier Ring Correlation from two replicas of the same image.

Parameters:

  • i_1 (np.ndarray) – ISM dataset (Nx x Ny x Nt x Nch)

  • max_iter (int) – Number of iteration

  • pad (np.array(Nx x Ny x Nch)) – Number of pixels used for zer-padding the image on each side

  • epsilon (float) – Minimum value of the denominator. Used to avoid division by zero (default = float.eps)

  • reg (float) – Regularization parameter (Tikhonov)

Returns:

img_deconv – Deconvolved image

Return type:

np.array(Nx x Ny)

FRC_MultiImg_RL_FFT_2(i_1, i_2, max_iter=50, pad=None, epsilon=None, reg=0)[source]

Multi-image Richardson-Lucy deconvolution, performed using FFT. It deconvolves each image of the dataset, returning Nch deconvoluted images. The PSF is automatically estimated with Fourier Ring Correlation from two replicas of the same image.

Parameters:

  • i_1 (np.array(Nx x Ny x Nch)) – ISM dataset

  • i_2 (np.array(Nx x Ny x Nch)) – ISM dataset

  • max_iter (int) – Number of iterations

  • pad (np.array(Nx x Ny x Nch)) – Number of pixels used for zer-padding the image on each side

  • epsilon (float) – Minimum value of the denominator. Used to avoid division by zero (default = float.eps)

  • reg (float) – Regularization parameter (Tikhonov)

Returns:

img_deconv – Deconvolved image

Return type:

np.array(Nx x Ny x Nch)

MultiImg_RL_FFT(h, i, bkg=None, max_iter=50, pad=None, epsilon=None, reg=0, out='last')[source]

Multi-image Richardson-Lucy deconvolution, performed using FFT. It deconvolves the entire dataset, returning a single deconvoluted image.

Parameters:

  • h (np.array(Nz x Nx x Ny x Nch)) – PSFs of the system. Nz is optional.

  • i (np.array(Nz x Nx x Ny x Nch)) – ISM dataset. Nz is optional.

  • max_iter (float) – Number of iterations

  • pad (int) – Number of pixels used for zero-padding the images on each side

  • epsilon (float) – Minimum value of the denominator. Used to avoid division by zero (default = float.eps)

  • reg (float) – Regularization parameter (Tikhonov)

Returns:

img_deconv – Deconvolved image. max_iter and Nz are optional.

Return type:

np.array(max_iter x Nz x Nx x Ny)

MultiImg_RL_FFT_2(h, i, max_iter=50, pad=None, epsilon=None, reg=0)[source]

Multi-image Richardson-Lucy deconvolution, performed using FFT. It deconvolves each image of the dataset, returning Nch deconvoluted images.

Parameters:

  • h (np.array(Nx x Ny x Nch)) – PSFs of the system

  • i (np.array(Nx x Ny x Nch)) – ISM dataset

  • max_iter (int) – Number of iterations

  • pad (np.array(Nx x Ny x Nch)) – Number of pixels used for zer-padding the image on each side

  • epsilon (float) – Minimum value of the denominator. Used to avoid division by zero (default = float.eps)

  • reg (float) – Regularization parameter (Tikhonov)

Returns:

img_deconv – Deconvolved image

Return type:

np.array(Nx x Ny x Nch)

PSF_FRC(i_1, i_2)[source]

PSFs estimation with Fourier Ring Correlation from two replicas of the same image.

Parameters:

  • i_1 (np.array(Nx x Ny x Nch)) – ISM dataset

  • i_2 (np.array(Nx x Ny x Nch)) – ISM dataset

Returns:

psf_frc – Estimated PSFs

Return type:

np.array(Nx x Ny x Nch)

PadDataset(img, pad_width)[source]

It pads the ISM dataset on each side of each image with pad_width pixels.

Parameters:

  • img (np.array(Nx x Ny x Nch)) – ISM dataset

  • pad_width (int) – Number of pixels used for zero-padding the images on each side

Returns:

img_deconv – Padded dataset

Return type:

np.array(Nx + 2*pad_width x Ny + 2*pad_width x Nch)

UnpadDataset(img, pad_width)[source]

It removes the padding from an ISM.

Parameters:

  • img (np.array(Nx + 2*pad_width x Ny + 2*pad_width x Nch)) – ISM dataset

  • pad_width (int) – Number of pixels used for zero-padding the images on each side

Returns:

img_deconv – Unpadded dataset

Return type:

np.array(Nx x Ny x Nch)

convolution_matrix(K, I)[source]

It calculates the matrix corresponding to the convolution with kernel K, to be applied to the flattened version of the input image I

Parameters:

  • K (np.array (Nx x Ny)) – Kernel of the convolution

  • I (np.array(Mx x My)) – Image

Returns:

  • Conv_matrix (np.array( Nx + Mx - 1 x Ny + My -1 )) – Convolution matrix

  • Img_flatten (np.array( Mx * My )) – Padded and flattened version of the input image # CHECK SHAPE

deconv_RL_FFT(h, i, max_iter=50, epsilon=None, reg=0, out='last')[source]

Richardson-Lucy deconvolution, performed using FFT

Parameters:

  • h (np.array (Nx x Ny)) – PSF of the system

  • i (np.array(Mx x My)) – Image

  • max_iter (float) – Number of iterations

  • epsilon (float) – Minimum value of the denominator. Used to avoid division by zero (default = float.eps)

  • reg (float) – Regularization parameter (Tikhonov)

Returns:

img_deconv – Deconvolved image

Return type:

np.array(Mx x My)

deconv_Wiener(h, i, reg=0, regularization='Tikhonov')[source]

Wiener deconvolution, performed using matrix multiplication

Parameters:

  • h (np.array (Nx x Ny)) – PSF of the system

  • i (np.array(Mx x My)) – Image

  • reg (float) – Regularization parameter

  • regularization (str) – Method for regularizing the algorithm ‘Tikhonov’ or ‘Laplace’

Returns:

img_deconv – Deconvolved image

Return type:

np.array(Mx x My)

deconv_Wiener_FFT(h, i, reg=0)[source]

Wiener deconvolution, performed using FFT

Parameters:

  • h (np.array (Nx x Ny)) – PSF of the system

  • i (np.array(Mx x My)) – Image

  • reg (float) – Regularization parameter (Tikhonov)

Returns:

img_deconv – Deconvolved image

Return type:

np.array(Mx x My)

disk2d(X, Y, mux, muy, T)[source]

2D disk function

Parameters:

  • X (np.array (Nx x Ny)) – meshgrid of the x-coordinate

  • Y (np.array (Nx x Ny)) – meshgrid of the y-coordinate

  • mux (int) – center on the x-axis

  • muy (int) – center on the y-axis

  • T (float) – radius of the disk

Returns:

disk – Disk

Return type:

np.array(Nx x Ny)

gauss2d(X, Y, mux, muy, sigma)[source]

2D radially symmetric Gaussian function

Parameters:

  • x (np.array (Nx x Ny)) – meshgrid of the x-coordinate

  • y (np.array (Nx x Ny)) – meshgrid of the y-coordinate

  • mux (int) – center on the x-axis

  • muy (int) – center on the y-axis

  • sigma (float) – dev. standard

Returns:

gauss – Gaussian distribution

Return type:

np.array(Nx x Ny)