python 3.*
numpy
pyyaml
scipy
scikit-image
scikit-learn
matplotlib

get_blur_params(norm_rads, sod, sdd, pix_wid, convg_thresh=1e-06, bdary_mask_perc=5, pad_factor=[3, 3], mask=None, edge_type=None)
    Estimate parameters of point spread functions (PSF) that model X-ray source blur and detector blur from normalized radiographs of a straight sharp edge or two mutually perpendicular sharp edges. 
    
    This function is used to estimate parameters of the PSFs that model X-ray source blur and detector blur. It takes as input the normalized radiographs at multiple source to object distances (SOD) and source to detector distances (SDD). If each radiograph has a single straight edge, then the measurement must be repeated for two different, preferably perpendicular, orientations of the edge. Currently, only a single straight edge in a radiograph is verified to work. The case of perpendicular edges in a radiograph will be supported soon. For more details, please refer to the document listed in the references.  
    Parameters:
        norm_rads (list): Python list of normalized radiographs, each of type numpy.ndarray, at various SODs and SDDs.
        sod (list): List of source to object distances (SOD), each of type float, at which each normalized radiograph in the list norm_rads was acquired.  
        sdd (list): List of source to detector distances (SDD), each of type float, at which each normalized radiograph in the list norm_rads was acquired.
        pix_wid (float): Effective width of each detector pixel. Note that this is the effective pixel size given by dividing the physical width of each detector pixel by the zoom factor of the optical lens.
        convg_thresh (float): Convergence threshold for the minimizer in the last final step when estimating source, detector, and transmission parameters. The convergence threshold for the minimizer during the first two initialization steps is ten times this value. The iterations stop when the ratio of the reduction in the error function (cost value) and the magnitude of the error function is lower than convg_thresh. This is the parameter ftol that is specified in the options parameter of scipy.optimize.minimize. The optimizer used is L-BFGS-B.
        bdary_mask_perc (float): Percentage of image region in the normalized radiographs that must be excluded from blur estimation. Pixels are excluded (or masked) beginning from the outermost periphery of the image and working inwards until the specified percentage of pixels is reached.
        pad_factor (list): Pad factor is a list of two integers that determine the amount of padding that must be applied to the radiographs to reduce aliasing during convolution. The number of rows/columns after padding is equal to pad_factor[0]/pad_factor[1] times the number of rows/columns in each normalized radiograph before padding. For example, if the first element in pad_factor is 2, then the radiograph is padded to twice its size along the first dimension.  
        mask (numpy.ndarray): Boolean mask of the same shape as the radiograph that is used to exclude pixels from blur estimation. An example use case is if some pixels in the radiographs are bad, then those pixels can be excluded from blur estimation by setting the corresponding entries in mask to false and true otherwise.
        edge_type (str): Used to indicate whether there is a single straight edge or two mutually perpendicular edges in each radiograph. If edge_type is perpendicular, then each radiograph is assumed to have two mutually perpendicular edges and a single straight edge otherwise. Currently, choosing perpendicular as edge_type is not recommended since it isn't a verified functionality and may lead to unstable behavior.  
    
    Returns:
        dict: Estimated parameters of X-ray source PSF that is returned as a python dictionary. It consists of several key-value pairs. The value for key source_FWHM_x_axis is the full width half maximum (FWHM) of the source PSF along the x-axis (i.e., second array dimension). The value for key source_FWHM_y_axis is the FWHM of source PSF along the y-axis (i.e., first array dimension). All FWHMs are for the source PSF in the plane of the X-ray source (and not the plane of the detector). The value for key cutoff_FWHM_multiplier decides the non-zero spatial extent of the exponential PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of cutoff_FWHM_multiplier times half the maximum FWHM (maximum of source_FWHM_x_axis and source_FWHM_y_axis).
        dict: Estimated parameters of detector PSF that is returned as a python dictionary. It consists of several key-value pairs. The value for key detector_FWHM_1 is the FWHM of the first exponential in the mixture density model for detector blur. The first exponential is the most dominant part of detector blur. The value for key detector_FWHM_2 is the FWHM of the second exponential in the mixture density model. This exponential has the largest FWHM and models the long running tails of the detector blur's PSF. The value for key detector_weight_1 is between 0 and 1 and is an approximate measure of the amount of contribution of the first exponential to the detector blur. The values for keys cutoff_FWHM_1_multiplier and cutoff_FWHM_2_multiplier decide the non-zero spatial extent of the detector PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of the maximum of cutoff_FWHM_1_multiplier*detector_FWHM_1/2 and cutoff_FWHM_2_multiplier*detector_FWHM_2/2.
        list: Estimated parameters of the transmission function for each input radiograph. This return value is a list of lists, where each inner nested list consists of two parameters of type float. These float values give the low and high values respectively of the transmission function. The number of nested lists in the returned list equals the number of input radiographs. Note that the transmission function is the normalized radiograph image that would have resulted in the absence of blur and noise.

get_trans_fit(norm_rad, sod, sdd, pix_wid, src_params, det_params, trans_params, pad_factor=[3, 3], edge_type=None)
    For a measured radiograph consisting of a straight sharp edge or two mutually perpendicular edges, get the ideal transmission function and a prediction from the blur model for the normalized radiograph in the presence of X-ray source and detector blurs. 
    
    Parameters:
        norm_rad (numpy.ndarray): Normalized radiograph
        sod (float): Source to object distance (SOD) for the radiograph norm_rad.
        sdd (float): Source to detector distance (SDD) for the radiograph norm_rad.
        pix_wid (float): Effective width of each detector pixel. Note that this is the effective pixel size given by dividing the physical width of each detector pixel by the zoom factor of the optical lens.
        src_params (dict): Estimated parameters of X-ray source PSF. It should consist of several key-value pairs. The value for key source_FWHM_x_axis is the full width half maximum (FWHM) of the source PSF along the x-axis (i.e., second array dimension). The value for key source_FWHM_y_axis is the FWHM of source PSF along the y-axis (i.e., first array dimension). All FWHMs are for the source PSF in the plane of the X-ray source (and not the detector plane). The value for key cutoff_FWHM_multiplier decides the non-zero spatial extent of the source blur PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of cutoff_FWHM_multiplier times half the maximum FWHM (maximum of source_FWHM_x_axis and source_FWHM_y_axis).
        det_params (dict): Estimated parameters of detector blur PSF. It should consist of several key-value pairs. The value for key detector_FWHM_1 is the FWHM of the first exponential in the mixture density model for detector blur. The first exponential is the most dominant part of detector blur. The value for key detector_FWHM_2 is the FWHM of the second exponential in the mixture density model. This exponential has the largest FWHM and models the long running tails of the detector blur's point spread function (PSF). The value for key detector_weight_1 is between 0 and 1 and is an approximate measure of the amount of contribution of the first exponential to the detector blur. The values for keys cutoff_FWHM_1_multiplier and cutoff_FWHM_2_multiplier decide the non-zero spatial extent of the detector PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of the maximum of cutoff_FWHM_1_multiplier*detector_FWHM_1/2 and cutoff_FWHM_2_multiplier*detector_FWHM_2/2.
        trans_params (list): A two element integer list of transmission function parameters. The first element is the low value and the second element is the high value of the transmission function. Note that the transmission func
        pad_factor (list): Pad factor is a list of two integers that determine the amount of padding that must be applied to the radiographs to reduce aliasing during convolution. The number of rows/columns after padding is equal to pad_factor[0]/pad_factor[1] times the number of rows/columns in each normalized radiograph before padding. For example, if the first element in pad_factor is 2, then the radiograph is padded to twice its size along the first dimension.  
        edge_type (str): Used to indicate whether there is a single straight edge or two mutually perpendicular edges in each radiograph. If edge_type is perpendicular, then each radiograph is assumed to have two mutually perpendicular edges and a single straight edge otherwise. Currently, choosing perpendicular as edge_type is not recommended since it isn't a verified functionality and may lead to unstable behavior.

get_source_psf(pix_wid, src_params, sod=1, sdd=2)
    Get point spread function (PSF) of X-ray source blur.
    
    Parameters:
        pix_wid (float): Effective width of each detector pixel. Note that this is the effective pixel size given by dividing the physical width of each detector pixel by the zoom factor of the optical lens.
        src_params (dict): Estimated parameters of X-ray source PSF. It should consist of several key-value pairs. The value for key source_FWHM_x_axis is the full width half maximum (FWHM) of the source PSF along the x-axis (i.e., second array dimension). The value for key source_FWHM_y_axis is the FWHM of source PSF along the y-axis (i.e., first array dimension). All FWHMs are for the source PSF in the plane of the X-ray source (and not the detector plane). The value for key cutoff_FWHM_multiplier decides the non-zero spatial extent of the source blur PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of cutoff_FWHM_multiplier times half the maximum FWHM (maximum of source_FWHM_x_axis and source_FWHM_y_axis).
        sod (float): Source to object distance (SOD) is necessary to compute PSF of source blur in the plane of the detector. Use the default value to compute source PSF at the plane of the X-ray source. Or, if sdd = 2*sod, then source blur PSF at the detector is same as the source blur PSF at the plane of the X-ray source. 
        sdd (float): Source to detector distance (SDD) is necessary to compute PSF of source blur in the plane of the detector. Use the default value to compute source PSF at the plane of the X-ray source. Or, if sdd = 2*sod, then source blur PSF at the detector is same as the source blur PSF at the plane of the X-ray source.
    
    Returns:
        numpy.ndarray: 2D array of source blur PSF

get_detector_psf(pix_wid, det_params)
    Get point spread function (PSF) of detector blur
    
    Parameters:
        pix_wid (float): Effective width of each detector pixel. Note that this is the effective pixel size given by dividing the physical width of each detector pixel by the zoom factor of the optical lens.
        det_params (dict): Estimated parameters of detector blur PSF. It should consist of several key-value pairs. The value for key detector_FWHM_1 is the FWHM of the first exponential in the mixture density model for detector blur. The first exponential is the most dominant part of detector blur. The value for key detector_FWHM_2 is the FWHM of the second exponential in the mixture density model. This exponential has the largest FWHM and models the long running tails of the detector blur's point spread function (PSF). The value for key detector_weight_1 is between 0 and 1 and is an approximate measure of the amount of contribution of the first exponential to the detector blur. The values for keys cutoff_FWHM_1_multiplier and cutoff_FWHM_2_multiplier decide the non-zero spatial extent of the detector PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of the maximum of cutoff_FWHM_1_multiplier*detector_FWHM_1/2 and cutoff_FWHM_2_multiplier*detector_FWHM_2/2.
    
    Returns:
        numpy.ndarray: 2D array of detector blur PSF

get_effective_psf(pix_wid, src_params, det_params, sod=1, sdd=2)
    Get point spread function (PSF) of the combined effect of X-ray source and detector blur.
    
    Parameters:
        pix_wid (float): Effective width of each detector pixel. Note that this is the effective pixel size given by dividing the physical width of each detector pixel by the zoom factor of the optical lens.
        src_params (dict): Estimated parameters of X-ray source PSF. It should consist of several key-value pairs. The value for key source_FWHM_x_axis is the full width half maximum (FWHM) of the source PSF along the x-axis (i.e., second array dimension). The value for key source_FWHM_y_axis is the FWHM of source PSF along the y-axis (i.e., first array dimension). All FWHMs are for the source PSF in the plane of the X-ray source (and not the detector plane). The value for key cutoff_FWHM_multiplier decides the non-zero spatial extent of the source blur PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of cutoff_FWHM_multiplier times half the maximum FWHM (maximum of source_FWHM_x_axis and source_FWHM_y_axis).
        det_params (dict): Estimated parameters of detector blur PSF. It should consist of several key-value pairs. The value for key detector_FWHM_1 is the FWHM of the first exponential in the mixture density model for detector blur. The first exponential is the most dominant part of detector blur. The value for key detector_FWHM_2 is the FWHM of the second exponential in the mixture density model. This exponential has the largest FWHM and models the long running tails of the detector blur's point spread function (PSF). The value for key detector_weight_1 is between 0 and 1 and is an approximate measure of the amount of contribution of the first exponential to the detector blur. The values for keys cutoff_FWHM_1_multiplier and cutoff_FWHM_2_multiplier decide the non-zero spatial extent of the detector PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of the maximum of cutoff_FWHM_1_multiplier*detector_FWHM_1/2 and cutoff_FWHM_2_multiplier*detector_FWHM_2/2.
        sod (float): Source to object distance (SOD) is necessary to compute PSF of source blur in the plane of the detector. Use the default value to compute source PSF at the plane of the X-ray source. Or, if sdd = 2*sod, then source blur PSF at the detector is same as the source blur PSF at the plane of the X-ray source. 
        sdd (float): Source to detector distance (SDD) is necessary to compute PSF of source blur in the plane of the detector. Use the default value to compute source PSF at the plane of the X-ray source. Or, if sdd = 2*sod, then source blur PSF at the detector is same as the source blur PSF at the plane of the X-ray source.
    
    Returns:
        numpy.ndarray: 2D array of effective blur PSF

wiener_deblur(norm_rad, sod, sdd, pix_wid, src_params, det_params, reg_param)
    Function to reduce blur (deblur) in a radiograph using Wiener filtering.     
    
    Parameters:
        norm_rad (numpy.ndarray): Normalized radiograph to deblur
        sod (float): Source to object distance (SOD) of the radiograph
        sdd (float): Source to detector distance (SDD) of the radiograph
        pix_wid (float): Effective width of each detector pixel. Note that this is the effective pixel size given by dividing the physical width of each detector pixel by the zoom factor of the optical lens.
        src_params (dict): Estimated parameters of X-ray source PSF. It should consist of several key-value pairs. The value for key source_FWHM_x_axis is the full width half maximum (FWHM) of the source PSF along the x-axis (i.e., second array dimension). The value for key source_FWHM_y_axis is the FWHM of source PSF along the y-axis (i.e., first array dimension). All FWHMs are for the source PSF in the plane of the X-ray source (and not the detector plane). The value for key cutoff_FWHM_multiplier decides the non-zero spatial extent of the source blur PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of cutoff_FWHM_multiplier times half the maximum FWHM (maximum of source_FWHM_x_axis and source_FWHM_y_axis).
        det_params (dict): Estimated parameters of detector blur PSF. It should consist of several key-value pairs. The value for key detector_FWHM_1 is the FWHM of the first exponential in the mixture density model for detector blur. The first exponential is the most dominant part of detector blur. The value for key detector_FWHM_2 is the FWHM of the second exponential in the mixture density model. This exponential has the largest FWHM and models the long running tails of the detector blur's point spread function (PSF). The value for key detector_weight_1 is between 0 and 1 and is an approximate measure of the amount of contribution of the first exponential to the detector blur. The values for keys cutoff_FWHM_1_multiplier and cutoff_FWHM_2_multiplier decide the non-zero spatial extent of the detector PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of the maximum of cutoff_FWHM_1_multiplier*detector_FWHM_1/2 and cutoff_FWHM_2_multiplier*detector_FWHM_2/2.
        reg_param (float): Regularization parameter for Wiener filtering deblurring algorithm. Noise and ringing artifacts in the deblurred radiograph decreases with increasing values for reg_param and vice versa. But, note that increasing reg_param can also result in excessive blurring due to over-regulization. It is recommended to empirically choose this parameter by increasing or decreasing it by a factor, greater than one (such as 2 or 10), until the desired image quality is achieved.
    
    Returns:
        numpy.ndarray: Deblurred radiograph using a Wiener filter.

least_squares_deblur(norm_rad, sod, sdd, pix_wid, src_params, det_params, reg_param, init_rad=None, weights=None, convg_thresh=0.01)
    Function to reduce blur (deblur) in radiographs using a regularized least squares iterative algorithm.     
    
    Parameters:
        norm_rad (numpy.ndarray): Normalized radiograph to deblur
        sod (float): Source to object distance (SOD) of the radiograph
        sdd (float): Source to detector distance (SDD) of the radiograph
        pix_wid (float): Effective width of each detector pixel. Note that this is the effective pixel size given by dividing the physical width of each detector pixel by the zoom factor of the optical lens.
        src_params (dict): Estimated parameters of X-ray source PSF. It should consist of several key-value pairs. The value for key source_FWHM_x_axis is the full width half maximum (FWHM) of the source PSF along the x-axis (i.e., second array dimension). The value for key source_FWHM_y_axis is the FWHM of source PSF along the y-axis (i.e., first array dimension). All FWHMs are for the source PSF in the plane of the X-ray source (and not the detector plane). The value for key cutoff_FWHM_multiplier decides the non-zero spatial extent of the source blur PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of cutoff_FWHM_multiplier times half the maximum FWHM (maximum of source_FWHM_x_axis and source_FWHM_y_axis).
        det_params (dict): Estimated parameters of detector blur PSF. It should consist of several key-value pairs. The value for key detector_FWHM_1 is the FWHM of the first exponential in the mixture density model for detector blur. The first exponential is the most dominant part of detector blur. The value for key detector_FWHM_2 is the FWHM of the second exponential in the mixture density model. This exponential has the largest FWHM and models the long running tails of the detector blur's point spread function (PSF). The value for key detector_weight_1 is between 0 and 1 and is an approximate measure of the amount of contribution of the first exponential to the detector blur. The values for keys cutoff_FWHM_1_multiplier and cutoff_FWHM_2_multiplier decide the non-zero spatial extent of the detector PSF. The PSF is clipped to zero beginning at a distance, as measured from the PSF's origin, of the maximum of cutoff_FWHM_1_multiplier*detector_FWHM_1/2 and cutoff_FWHM_2_multiplier*detector_FWHM_2/2.
        reg_param (float): Regularization parameter for the least squares deblurring algorithm. Noise and ringing artifacts in the deblurred radiograph decreases with increasing values for reg_param and vice versa. But, note that increasing reg_param can also result in excessive blurring due to over-regulization. It is recommended to empirically choose this parameter by increasing or decreasing it by a factor, greater than one (such as 2 or 10), until the desired image quality is achieved.
        init_rad (numpy.ndarray): Initial estimate for the deblurred radiograph. If set to None, then the blurred radiograph is used as an initial estimate. If not None, then init_rad must be a numpy.ndarray of the same shape as norm_rad. 
        weights (numpy.ndarray): Used to increase or decrease reliance on a particular pixel of norm_rad in the forward model cost function. If set to None, every pixel is assigned the same weight of 1.
        convg_thresh (float): Convergence threshold for the minimizer used to deblur the input radiograph. The iterations stop when the ratio of the reduction in the error function (cost value) and the magnitude of the error function is lower than convg_thresh. This is the parameter ftol that is specified in the options parameter of scipy.optimize.minimize. The optimizer used is L-BFGS-B.
    
    Returns:
        numpy.ndarray: Deblurred radiograph using regularized least squares algorithm.