Deblur Radiographs¶

Once the parameters of source and detector PSFs are estimated, radiographs of any arbitrary sample acquired at any source to object distance (SOD) and source to detector distance (SDD) can be deblurred using various techniques.
To deblur a radiograph using Wiener filter, the function pysaber.wiener_deblur() is used. To deblur using regularized least squares deconvolution (RLSD), use the function pysaber.least_squares_deblur().
Deblurring increases sharpness and resolution. However, it also introduces ringing artifacts and increases noise. To reduce noise and ringing artifacts, the regularization parameter can be increased. Ringing artifacts also increase with increasing inaccuracy of the blur model. Thus, it is essential to obtain a good fit between the measured radiograph and the blur model prediction as explained in the section Validate Blur Model.
The python scripts shown below demonstrate deblurring of radiographs using Wiener filter and RLSD. To obtain the data that is required to run this script, download and unzip the zip file at the link data. To run the script as is within the current working directory, the files in the zip file must be placed within a folder called data.

Deblurring using Wiener filter¶

import numpy as np
from pysaber import wiener_deblur #To deblur using Wiener filtering
import matplotlib.pyplot as plt #To display images
from PIL import Image #To read images in TIFF format

rad_file = 'data/horz_edge_25mm.tif' #Filename of radiograph
bright_file = 'data/horz_bright.tif' #Bright field
dark_file = 'data/horz_dark.tif' #Dark field

sdd = 71003.08 #Source to detector distance (SDD) in micrometers
sod = 24751.89 #Source to object distance (SOD) in micrometers
pix_wid = 0.675 #Pixel width in micrometers
reg_param = 0.1 #Regularization parameter

rad = np.asarray(Image.open(rad_file)) #Read radiograph and convert to numpy array
bright = np.asarray(Image.open(bright_file)) #Read bright field image and convert to numpy array
dark = np.asarray(Image.open(dark_file)) #Read dark field image and convert to numpy array
norm_rad = (rad-dark)/(bright-dark) #Normalize radiograph

#X-ray source blur parameters
src_params = {'source_FWHM_x_axis':2.69,
                'source_FWHM_y_axis':3.01, 
                'norm_power':1.0,
                'cutoff_FWHM_multiplier':10}

#Detector blur parameters
det_params = {'detector_FWHM_1':1.85, 
                'detector_FWHM_2':126.5, 
                'detector_weight_1':0.916, 
                'norm_power':1.0, 
                'cutoff_FWHM_1_multiplier':10, 
                'cutoff_FWHM_2_multiplier':10}

#Deblur the radiograph using Wiener filter
wiener_rad = wiener_deblur(norm_rad,sod,sdd-sod,pix_wid,src_params,det_params,reg_param)

#Display deblurred radiograph
sz = wiener_rad.shape
x = np.arange(-(sz[1]//2),(sz[1]//2)+1,1)*pix_wid
y = np.arange(-(sz[0]//2),(sz[0]//2)+1,1)*pix_wid
plt.pcolormesh(x,y,wiener_rad,cmap='gray')
plt.xlabel('micrometers')
plt.ylabel('micrometers')
plt.title('Wiener deblur')
plt.colorbar()
plt.show()

Deblurring using Regularized Least Squares Deconvolution¶

import numpy as np
from pysaber import least_squares_deblur #To deblur using regularized least squares deconvolution (RLSD)
import matplotlib.pyplot as plt #To display images
from PIL import Image #To read images in TIFF format

rad_file = 'data/horz_edge_25mm.tif' #Filename of radiograph
bright_file = 'data/horz_bright.tif' #Bright field image
dark_file = 'data/horz_dark.tif' #Dark field image

sdd = 71003.08 #Source to detector distance (SDD) in micrometers
sod = 24751.89 #Source to object distance (SOD) in micrometers
pix_wid = 0.675 #Pixel width in micrometers
reg_param = 0.001 #Regularization parameter

rad = np.asarray(Image.open(rad_file)) #Read radiograph and convert to numpy array
bright = np.asarray(Image.open(bright_file)) #Read bright field image and convert to numpy array
dark = np.asarray(Image.open(dark_file)) #Read dark field image and convert to numpy array
norm_rad = (rad-dark)/(bright-dark) #Normalize radiograph

#X-ray source blur parameters
src_params = {'source_FWHM_x_axis':2.69,
                'source_FWHM_y_axis':3.01, 
                'norm_power':1.0,
                'cutoff_FWHM_multiplier':10}

#Detector blur parameters
det_params = {'detector_FWHM_1':1.85, 
                'detector_FWHM_2':126.5, 
                'detector_weight_1':0.916, 
                'norm_power':1.0, 
                'cutoff_FWHM_1_multiplier':10, 
                'cutoff_FWHM_2_multiplier':10}

#Deblur the radiograph using regularized least squares deconvolution (RLSD)
rlsd_rad = least_squares_deblur(norm_rad,sod,sdd-sod,pix_wid,src_params,det_params,reg_param,thresh=2e-4)

#Display deblurred radiograph of artifact
sz = rlsd_rad.shape
x = np.arange(-(sz[1]//2),(sz[1]//2)+1,1)*pix_wid
y = np.arange(-(sz[0]//2),(sz[0]//2)+1,1)*pix_wid
plt.pcolormesh(x,y,rlsd_rad,cmap='gray')
plt.xlabel('micrometers')
plt.ylabel('micrometers')
plt.title('RLSD deblur')
plt.colorbar()
plt.show()