denoise
¶
bench 
Run benchmarks for module using nose. 
test 
Run tests for module using nose. 
Module: denoise.adaptive_soft_matching
¶
adaptive_soft_matching (ima, fimau, fimao, sigma) 
Adaptive Soft Coefficient Matching 
Module: denoise.localpca
¶
eigh (a[, b, lower, eigvals_only, …]) 
Solve an ordinary or generalized eigenvalue problem for a complex Hermitian or real symmetric matrix. 
localpca (arr, sigma[, mask, pca_method, …]) 
Local PCAbased denoising of diffusion datasets. 
Module: denoise.nlmeans
¶
nlmeans (arr, sigma[, mask, patch_radius, …]) 
Nonlocal means for denoising 3D and 4D images 
nlmeans_3d 
Nonlocal means for denoising 3D images 
Module: denoise.noise_estimate
¶
convolve (input, weights[, output, mode, …]) 
Multidimensional convolution. 
estimate_sigma (arr[, …]) 
Standard deviation estimation from local patches 
piesno (data, N[, alpha, l, itermax, eps, …]) 
Probabilistic Identification and Estimation of Noise (PIESNO). 
Module: denoise.non_local_means
¶
nlmeans_block 
NonLocal Means Denoising Using Blockwise Averaging 
non_local_means (arr, sigma[, mask, …]) 
Nonlocal means for denoising 3D and 4D images, using 
bench¶

dipy.denoise.
bench
(label='fast', verbose=1, extra_argv=None)¶ Run benchmarks for module using nose.
Parameters:  label : {‘fast’, ‘full’, ‘’, attribute identifier}, optional
Identifies the benchmarks to run. This can be a string to pass to the nosetests executable with the ‘A’ option, or one of several special values. Special values are: * ‘fast’  the default  which corresponds to the
nosetests A
option of ‘not slow’.
 ‘full’  fast (as above) and slow benchmarks as in the ‘no A’ option to nosetests  this is the same as ‘’.
 None or ‘’  run all tests.
attribute_identifier  string passed directly to nosetests as ‘A’.
 verbose : int, optional
Verbosity value for benchmark outputs, in the range 110. Default is 1.
 extra_argv : list, optional
List with any extra arguments to pass to nosetests.
Returns:  success : bool
Returns True if running the benchmarks works, False if an error occurred.
Notes
Benchmarks are like tests, but have names starting with “bench” instead of “test”, and can be found under the “benchmarks” subdirectory of the module.
Each NumPy module exposes bench in its namespace to run all benchmarks for it.
Examples
>>> success = np.lib.bench() Running benchmarks for numpy.lib ... using 562341 items: unique: 0.11 unique1d: 0.11 ratio: 1.0 nUnique: 56230 == 56230 ... OK
>>> success True
test¶

dipy.denoise.
test
(label='fast', verbose=1, extra_argv=None, doctests=False, coverage=False, raise_warnings=None, timer=False)¶ Run tests for module using nose.
Parameters:  label : {‘fast’, ‘full’, ‘’, attribute identifier}, optional
Identifies the tests to run. This can be a string to pass to the nosetests executable with the ‘A’ option, or one of several special values. Special values are: * ‘fast’  the default  which corresponds to the
nosetests A
option of ‘not slow’.
 ‘full’  fast (as above) and slow tests as in the ‘no A’ option to nosetests  this is the same as ‘’.
 None or ‘’  run all tests.
attribute_identifier  string passed directly to nosetests as ‘A’.
 verbose : int, optional
Verbosity value for test outputs, in the range 110. Default is 1.
 extra_argv : list, optional
List with any extra arguments to pass to nosetests.
 doctests : bool, optional
If True, run doctests in module. Default is False.
 coverage : bool, optional
If True, report coverage of NumPy code. Default is False. (This requires the `coverage module:
 raise_warnings : None, str or sequence of warnings, optional
This specifies which warnings to configure as ‘raise’ instead of being shown once during the test execution. Valid strings are:
 “develop” : equals
(Warning,)
 “release” : equals
()
, don’t raise on any warnings.
The default is to use the class initialization value.
 “develop” : equals
 timer : bool or int, optional
Timing of individual tests with
nosetimer
(which needs to be installed). If True, time tests and report on all of them. If an integer (sayN
), report timing results forN
slowest tests.
Returns:  result : object
Returns the result of running the tests as a
nose.result.TextTestResult
object.
Notes
Each NumPy module exposes test in its namespace to run all tests for it. For example, to run all tests for numpy.lib:
>>> np.lib.test()
Examples
>>> result = np.lib.test() Running unit tests for numpy.lib ... Ran 976 tests in 3.933s
OK
>>> result.errors [] >>> result.knownfail []
adaptive_soft_matching¶

dipy.denoise.adaptive_soft_matching.
adaptive_soft_matching
(ima, fimau, fimao, sigma)¶ Adaptive Soft Coefficient Matching
Combines two filtered 3Dimages at different resolutions and the orginal image. Returns the resulting combined image.
Parameters:  ima : the original (not filtered) image
 fimau : 3D double array,
filtered image with optimized nonlocal means using a small block (suggested:3x3), which corresponds to a “high resolution” filter.
 fimao : 3D double array,
filtered image with optimized nonlocal means using a small block (suggested:5x5), which corresponds to a “low resolution” filter.
 sigma : the estimated standard deviation of the Gaussian random variables
that explain the rician noise. Note: In P. Coupe et al. the rician noise was simulated as sqrt((f+x)^2 + (y)^2) where f is the pixel value and x and y are independent realizations of a random variable with Normal distribution, with mean=0 and standard deviation=h
Returns:  fima : 3D double array
output denoised array which is of the same shape as that of the input
References
[Coupe11] Pierrick Coupe, Jose Manjon, Montserrat Robles, Louis Collins. “Multiresolution NonLocal Means Filter for 3D MR Image Denoising” IET Image Processing, Institution of Engineering and Technology, 2011
eigh¶

dipy.denoise.localpca.
eigh
(a, b=None, lower=True, eigvals_only=False, overwrite_a=False, overwrite_b=False, turbo=True, eigvals=None, type=1, check_finite=True)¶ Solve an ordinary or generalized eigenvalue problem for a complex Hermitian or real symmetric matrix.
Find eigenvalues w and optionally eigenvectors v of matrix a, where b is positive definite:
a v[:,i] = w[i] b v[:,i] v[i,:].conj() a v[:,i] = w[i] v[i,:].conj() b v[:,i] = 1
Parameters:  a : (M, M) array_like
A complex Hermitian or real symmetric matrix whose eigenvalues and eigenvectors will be computed.
 b : (M, M) array_like, optional
A complex Hermitian or real symmetric definite positive matrix in. If omitted, identity matrix is assumed.
 lower : bool, optional
Whether the pertinent array data is taken from the lower or upper triangle of a. (Default: lower)
 eigvals_only : bool, optional
Whether to calculate only eigenvalues and no eigenvectors. (Default: both are calculated)
 turbo : bool, optional
Use divide and conquer algorithm (faster but expensive in memory, only for generalized eigenvalue problem and if eigvals=None)
 eigvals : tuple (lo, hi), optional
Indexes of the smallest and largest (in ascending order) eigenvalues and corresponding eigenvectors to be returned: 0 <= lo <= hi <= M1. If omitted, all eigenvalues and eigenvectors are returned.
 type : int, optional
Specifies the problem type to be solved:
type = 1: a v[:,i] = w[i] b v[:,i]
type = 2: a b v[:,i] = w[i] v[:,i]
type = 3: b a v[:,i] = w[i] v[:,i]
 overwrite_a : bool, optional
Whether to overwrite data in a (may improve performance)
 overwrite_b : bool, optional
Whether to overwrite data in b (may improve performance)
 check_finite : bool, optional
Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, nontermination) if the inputs do contain infinities or NaNs.
Returns:  w : (N,) float ndarray
The N (1<=N<=M) selected eigenvalues, in ascending order, each repeated according to its multiplicity.
 v : (M, N) complex ndarray
(if eigvals_only == False)
The normalized selected eigenvector corresponding to the eigenvalue w[i] is the column v[:,i].
Normalization:
type 1 and 3: v.conj() a v = w
type 2: inv(v).conj() a inv(v) = w
type = 1 or 2: v.conj() b v = I
type = 3: v.conj() inv(b) v = I
Raises:  LinAlgError
If eigenvalue computation does not converge, an error occurred, or b matrix is not definite positive. Note that if input matrices are not symmetric or hermitian, no error is reported but results will be wrong.
See also
eigvalsh
 eigenvalues of symmetric or Hermitian arrays
eig
 eigenvalues and right eigenvectors for nonsymmetric arrays
eigh
 eigenvalues and right eigenvectors for symmetric/Hermitian arrays
eigh_tridiagonal
 eigenvalues and right eiegenvectors for symmetric/Hermitian tridiagonal matrices
Notes
This function does not check the input array for being hermitian/symmetric in order to allow for representing arrays with only their upper/lower triangular parts.
Examples
>>> from scipy.linalg import eigh >>> A = np.array([[6, 3, 1, 5], [3, 0, 5, 1], [1, 5, 6, 2], [5, 1, 2, 2]]) >>> w, v = eigh(A) >>> np.allclose(A @ v  v @ np.diag(w), np.zeros((4, 4))) True
localpca¶

dipy.denoise.localpca.
localpca
(arr, sigma, mask=None, pca_method='eig', patch_radius=2, tau_factor=2.3, out_dtype=None)¶ Local PCAbased denoising of diffusion datasets.
Parameters:  arr : 4D array
Array of data to be denoised. The dimensions are (X, Y, Z, N), where N are the diffusion gradient directions.
 mask : 3D boolean array
A mask with voxels that are true inside the brain and false outside of it. The function denoises within the true part and returns zeros outside of those voxels.
 sigma : float or 3D array
Standard deviation of the noise estimated from the data.
 pca_method : ‘eig’ or ‘svd’
Use either eigenvalue decomposition (eig) or singular value decomposition (svd) for principal component analysis. The default method is ‘eig’ which is faster. However, occasionally ‘svd’ might be more accurate.
 patch_radius : int, optional
The radius of the local patch to be taken around each voxel (in voxels). Default: 2 (denoise in blocks of 5x5x5 voxels).
 tau_factor : float, optional
Thresholding of PCA eigenvalues is done by nulling out eigenvalues that are smaller than:
\[\tau = (\tau_{factor} \sigma)^2\]Default: 2.3, based on the results described in [Manjon13].
 out_dtype : str or dtype, optional
The dtype for the output array. Default: output has the same dtype as the input.
Returns:  denoised_arr : 4D array
This is the denoised array of the same size as that of the input data, clipped to nonnegative values
References
[Manjon13] (1, 2) Manjon JV, Coupe P, Concha L, Buades A, Collins DL (2013) Diffusion Weighted Image Denoising Using Overcomplete Local PCA. PLoS ONE 8(9): e73021. https://doi.org/10.1371/journal.pone.0073021
nlmeans¶

dipy.denoise.nlmeans.
nlmeans
(arr, sigma, mask=None, patch_radius=1, block_radius=5, rician=True, num_threads=None)¶ Nonlocal means for denoising 3D and 4D images
Parameters:  arr : 3D or 4D ndarray
The array to be denoised
 mask : 3D ndarray
 sigma : float or 3D array
standard deviation of the noise estimated from the data
 patch_radius : int
patch size is
2 x patch_radius + 1
. Default is 1. block_radius : int
block size is
2 x block_radius + 1
. Default is 5. rician : boolean
If True the noise is estimated as Rician, otherwise Gaussian noise is assumed.
 num_threads : int
Number of threads. If None (default) then all available threads will be used (all CPU cores).
Returns:  denoised_arr : ndarray
the denoised
arr
which has the same shape asarr
.
References
[Descoteaux08] Descoteaux, Maxim and WiestDaessle`, Nicolas and Prima, Sylvain and Barillot, Christian and Deriche, Rachid Impact of Rician Adapted NonLocal Means Filtering on HARDI, MICCAI 2008
nlmeans_3d¶

dipy.denoise.nlmeans.
nlmeans_3d
()¶ Nonlocal means for denoising 3D images
Parameters:  arr : 3D ndarray
The array to be denoised
 mask : 3D ndarray
 sigma : float or 3D array
standard deviation of the noise estimated from the data
 patch_radius : int
patch size is
2 x patch_radius + 1
. Default is 1. block_radius : int
block size is
2 x block_radius + 1
. Default is 5. rician : boolean
If True the noise is estimated as Rician, otherwise Gaussian noise is assumed.
 num_threads : int
Number of threads. If None (default) then all available threads will be used.
Returns:  denoised_arr : ndarray
the denoised
arr
which has the same shape asarr
.
convolve¶

dipy.denoise.noise_estimate.
convolve
(input, weights, output=None, mode='reflect', cval=0.0, origin=0)¶ Multidimensional convolution.
The array is convolved with the given kernel.
Parameters:  input : array_like
The input array.
 weights : array_like
Array of weights, same number of dimensions as input
 output : array or dtype, optional
The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created.
 mode : str or sequence, optional
The mode parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is ‘reflect’. The valid values and their behavior is as follows:
 ‘reflect’ (d c b a  a b c d  d c b a)
The input is extended by reflecting about the edge of the last pixel.
 ‘constant’ (k k k k  a b c d  k k k k)
The input is extended by filling all values beyond the edge with the same constant value, defined by the cval parameter.
 ‘nearest’ (a a a a  a b c d  d d d d)
The input is extended by replicating the last pixel.
 ‘mirror’ (d c b  a b c d  c b a)
The input is extended by reflecting about the center of the last pixel.
 ‘wrap’ (a b c d  a b c d  a b c d)
The input is extended by wrapping around to the opposite edge.
 cval : scalar, optional
Value to fill past edges of input if mode is ‘constant’. Default is 0.0
 origin : int or sequence, optional
Controls the placement of the filter on the input array’s pixels. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. By passing a sequence of origins with length equal to the number of dimensions of the input array, different shifts can be specified along each axis.
Returns:  result : ndarray
The result of convolution of input with weights.
See also
correlate
 Correlate an image with a kernel.
Notes
Each value in result is \(C_i = \sum_j{I_{i+kj} W_j}\), where W is the weights kernel, j is the nD spatial index over \(W\), I is the input and k is the coordinate of the center of W, specified by origin in the input parameters.
Examples
Perhaps the simplest case to understand is
mode='constant', cval=0.0
, because in this case borders (i.e. where the weights kernel, centered on any one value, extends beyond an edge of input.>>> a = np.array([[1, 2, 0, 0], ... [5, 3, 0, 4], ... [0, 0, 0, 7], ... [9, 3, 0, 0]]) >>> k = np.array([[1,1,1],[1,1,0],[1,0,0]]) >>> from scipy import ndimage >>> ndimage.convolve(a, k, mode='constant', cval=0.0) array([[11, 10, 7, 4], [10, 3, 11, 11], [15, 12, 14, 7], [12, 3, 7, 0]])
Setting
cval=1.0
is equivalent to padding the outer edge of input with 1.0’s (and then extracting only the original region of the result).>>> ndimage.convolve(a, k, mode='constant', cval=1.0) array([[13, 11, 8, 7], [11, 3, 11, 14], [16, 12, 14, 10], [15, 6, 10, 5]])
With
mode='reflect'
(the default), outer values are reflected at the edge of input to fill in missing values.>>> b = np.array([[2, 0, 0], ... [1, 0, 0], ... [0, 0, 0]]) >>> k = np.array([[0,1,0], [0,1,0], [0,1,0]]) >>> ndimage.convolve(b, k, mode='reflect') array([[5, 0, 0], [3, 0, 0], [1, 0, 0]])
This includes diagonally at the corners.
>>> k = np.array([[1,0,0],[0,1,0],[0,0,1]]) >>> ndimage.convolve(b, k) array([[4, 2, 0], [3, 2, 0], [1, 1, 0]])
With
mode='nearest'
, the single nearest value in to an edge in input is repeated as many times as needed to match the overlapping weights.>>> c = np.array([[2, 0, 1], ... [1, 0, 0], ... [0, 0, 0]]) >>> k = np.array([[0, 1, 0], ... [0, 1, 0], ... [0, 1, 0], ... [0, 1, 0], ... [0, 1, 0]]) >>> ndimage.convolve(c, k, mode='nearest') array([[7, 0, 3], [5, 0, 2], [3, 0, 1]])
estimate_sigma¶

dipy.denoise.noise_estimate.
estimate_sigma
(arr, disable_background_masking=False, N=0)¶ Standard deviation estimation from local patches
Parameters:  arr : 3D or 4D ndarray
The array to be estimated
 disable_background_masking : bool, default False
If True, uses all voxels for the estimation, otherwise, only nonzeros voxels are used. Useful if the background is masked by the scanner.
 N : int, default 0
Number of coils of the receiver array. Use N = 1 in case of a SENSE reconstruction (Philips scanners) or the number of coils for a GRAPPA reconstruction (Siemens and GE). Use 0 to disable the correction factor, as for example if the noise is Gaussian distributed. See [1] for more information.
Returns:  sigma : ndarray
standard deviation of the noise, one estimation per volume.
piesno¶

dipy.denoise.noise_estimate.
piesno
(data, N, alpha=0.01, l=100, itermax=100, eps=1e05, return_mask=False)¶ Probabilistic Identification and Estimation of Noise (PIESNO).
Parameters:  data : ndarray
The magnitude signals to analyse. The last dimension must contain the same realisation of the volume, such as dMRI or fMRI data.
 N : int
The number of phase array coils of the MRI scanner. If your scanner does a SENSE reconstruction, ALWAYS use N=1, as the noise profile is always Rician. If your scanner does a GRAPPA reconstruction, set N as the number of phase array coils.
 alpha : float
Probabilistic estimation threshold for the gamma function.
 l : int
number of initial estimates for sigma to try.
 itermax : int
Maximum number of iterations to execute if convergence is not reached.
 eps : float
Tolerance for the convergence criterion. Convergence is reached if two subsequent estimates are smaller than eps.
 return_mask : bool
If True, return a mask identyfing all the pure noise voxel that were found.
Returns:  sigma : float
The estimated standard deviation of the gaussian noise.
 mask : ndarray (optional)
A boolean mask indicating the voxels identified as pure noise.
References
[1] Koay CG, Ozarslan E and Pierpaoli C. “Probabilistic Identification and Estimation of Noise (PIESNO): A selfconsistent approach and its applications in MRI.” Journal of Magnetic Resonance 2009; 199: 94103.
[2] Koay CG, Ozarslan E and Basser PJ. “A signal transformational framework for breaking the noise floor and its applications in MRI.” Journal of Magnetic Resonance 2009; 197: 108119.
nlmeans_block¶

dipy.denoise.non_local_means.
nlmeans_block
()¶ NonLocal Means Denoising Using Blockwise Averaging
Parameters:  image : 3D array of doubles
the input image, corrupted with rician noise
 mask : 3D array of doubles
the input mask
 patch_radius : int
similar patches in the nonlocal means are searched for locally, inside a cube of side 2*v+1 centered at each voxel of interest.
 block_radius : int
the size of the block to be used (2*f+1)x(2*f+1)x(2*f+1) in the blockwise nonlocal means implementation (the Coupe’s proposal).
 h : double
the estimated amount of rician noise in the input image: in P. Coupe et al. the rician noise was simulated as sqrt((f+x)^2 + (y)^2) where f is the pixel value and x and y are independent realizations of a random variable with Normal distribution, with mean=0 and standard deviation=h
 rician : boolean
If True the noise is estimated as Rician, otherwise Gaussian noise is assumed.
Returns:  fima: 3D double array
the denoised output which has the same shape as input image.
References
 [1] P. Coupe, P. Yger, S. Prima, P. Hellier, C. Kervrann, C. Barillot,
 “An Optimized Blockwise Non Local Means Denoising Filter for 3D Magnetic Resonance Images” IEEE Transactions on Medical Imaging, 27(4):425441, 2008
 [2] Pierrick Coupe, Jose Manjon, Montserrat Robles, Louis Collins.
 “Multiresolution NonLocal Means Filter for 3D MR Image Denoising” IET Image Processing, Institution of Engineering and Technology, 2011
non_local_means¶

dipy.denoise.non_local_means.
non_local_means
(arr, sigma, mask=None, patch_radius=1, block_radius=5, rician=True)¶  Nonlocal means for denoising 3D and 4D images, using
 blockwise averaging approach
Parameters:  arr : 3D or 4D ndarray
The array to be denoised
 mask : 3D ndarray
 sigma : float
standard deviation of the noise estimated from the data
 patch_radius : int
patch size is
2 x patch_radius + 1
. Default is 1. block_radius : int
block size is
2 x block_radius + 1
. Default is 5. rician : boolean
If True the noise is estimated as Rician, otherwise Gaussian noise is assumed.
Returns:  denoised_arr : ndarray
the denoised
arr
which has the same shape asarr
.
References
[Coupe08] P. Coupe, P. Yger, S. Prima, P. Hellier, C. Kervrann, C. Barillot, An Optimized Blockwise Non Local Means Denoising Filter for 3D Magnetic Resonance Images, IEEE Transactions on Medical Imaging, 27(4):425441, 2008 [Coupe11] Pierrick Coupe, Jose Manjon, Montserrat Robles, Louis Collins. Adaptive Multiresolution NonLocal Means Filter for 3D MR Image Denoising IET Image Processing, Institution of Engineering and Technology, 2011