# Denoise images using Local PCA¶

The local PCA based denoising algorithm [Manjon2013] is an effective denoising method because it takes into account the directional information in diffusion data.

The basic idea behind local PCA based diffusion denoising can be explained in the following three basic steps:

• First, we estimate the local noise variance at each voxel.
• Then, we apply PCA in local patches around each voxel over the gradient directions.
• Finally, we threshold the eigenvalues based on the local estimate of sigma and then do a PCA reconstruction

import numpy as np
import nibabel as nib
import matplotlib.pyplot as plt
from time import time
from dipy.denoise.localpca import localpca
from dipy.denoise.pca_noise_estimate import pca_noise_estimate


Load one of the datasets. These data were acquired with 63 gradients and 1 non-diffusion (b=0) image.

img, gtab = read_isbi2013_2shell()

data = img.get_data()
affine = img.affine

print("Input Volume", data.shape)


We use the pca_noise_estimate method to estimate the value of sigma to be used in local PCA algorithm. It takes both data and the gradient table object as input and returns an estimate of local noise standard deviation as a 3D array. We return a smoothed version, where a Gaussian filter with radius 3 voxels has been applied to the estimate of the noise before returning it.

We correct for the bias due to Rician noise, based on an equation developed by Koay and Basser [Koay2006].

t = time()
sigma = pca_noise_estimate(data, gtab, correct_bias=True, smooth=3)
print("Sigma estimation time", time() - t)


Perform the localPCA using the function localpca.

The localpca algorithm takes into account for the directional information in the diffusion MR data. It performs PCA on local 4D patch and then thresholds it using the local variance estimate done by noise estimation function, then performing PCA reconstruction on it gives us the deniosed estimate.

t = time()

print("Time taken for local PCA (slow)", -t + time())


Let us plot the axial slice of the original and denoised data. We visualize all the slices (22 in total)

sli = data.shape[2] // 2
gra = data.shape[3] // 2
orig = data[:, :, sli, gra]
den = denoised_arr[:, :, sli, gra]
rms_diff = np.sqrt((orig - den) ** 2)

fig, ax = plt.subplots(1, 3)
ax[0].imshow(orig, cmap='gray', origin='lower', interpolation='none')
ax[0].set_title('Original')
ax[0].set_axis_off()
ax[1].imshow(den, cmap='gray', origin='lower', interpolation='none')
ax[1].set_title('Denoised Output')
ax[1].set_axis_off()
ax[2].imshow(rms_diff, cmap='gray', origin='lower', interpolation='none')
ax[2].set_title('Residual')
ax[2].set_axis_off()
plt.savefig('denoised_localpca.png', bbox_inches='tight')

print("The result saved in denoised_localpca.png")


Showing the middle axial slice of the local PCA denoised output.

nib.save(nib.Nifti1Image(denoised_arr,
affine), 'denoised_localpca.nii.gz')

print("Entire denoised data saved in denoised_localpca.nii.gz")

 [Manjon2013] Manjon JV, Coupe P, Concha L, Buades A, Collins DL “Diffusion Weighted Image Denoising Using Overcomplete Local PCA” (2013). PLoS ONE 8(9): e73021. doi:10.1371/journal.pone.0073021.
 [Koay2006] Koay CG, Basser PJ (2006). “Analytically exact correction scheme for signal extraction from noisy magnitude MR signals”. JMR 179: 317-322.

Example source code

You can download the full source code of this example. This same script is also included in the dipy source distribution under the doc/examples/ directory.