wavelet¶

Wrappers for PyWavelets.

mr_utils.utils.wavelet.cdf97_2d_forward(x, level, axes=(-2, -1))[source]¶

Forward 2D Cohen–Daubechies–Feauveau 9/7 wavelet.

Parameters:

x (array_like) – 2D signal.
level (int) – Decomposition level.
axes (tuple, optional) – Axes to perform wavelet decomposition across.

Returns:

wavelet_transform (array_like) – The stitched together elements wvlt (see combine_chunks).
locations (list) – Indices telling us how we stitched it together so we can take it back apart.

Notes

Returns transform, same shape as input, with locations. Locations is a list of indices instructing cdf97_2d_inverse where the coefficients for each block are located.

Biorthogonal 4/4 is the same as CDF 9/7 according to wikipedia [1].

References

[1]	https://en.wikipedia.org/wiki/ Cohen%E2%80%93Daubechies%E2%80%93Feauveau_wavelet#Numbering

mr_utils.utils.wavelet.cdf97_2d_inverse(coeffs, locations, axes=(-2, -1))[source]¶

Inverse 2D Cohen–Daubechies–Feauveau 9/7 wavelet.

Parameters:	coeffs (array_like) – Stitched together wavelet transform. locations (list) – Output of cdf97_2d_forward(). axes (tuple, optional) – Axes to perform wavelet transform across.
Returns:	Inverse CDF97 transform.
Return type:	array_like

mr_utils.utils.wavelet.combine_chunks(wvlt, shape, dtype=<class 'float'>)[source]¶

Stitch together the output of PyWavelets wavedec2.

Parameters:

wvlt (list of array_like) – Output of pywt.wavedec2().
shape (tuple) – Desired shape.
dtype (np.dtype, optional) – Type of numpy array.

Returns:

wavelet_transform (array_like) – The stitched together elements wvlt (see notes).
locations (list) – Indices telling us how we stitched it together so we can take it back apart.

Notes

We have tuples that look like this:
                            -------------------
                            |        |        |
                            | cA(LL) | cH(LH) |
                            |        |        |
(cA, (cH, cV, cD))  <--->   -------------------
                            |        |        |
                            | cV(HL) | cD(HH) |
                            |        |        |
                            -------------------

mr_utils.utils.wavelet.split_chunks(coeffs, locations)[source]¶

Separate the stitched together transform into blocks again.

Parameters:	x (array_like) – Stitched together wavelet transform. locations (list) – Indices where the coefficients for each block are located.
Returns:	coeff_list – List of coefficients of wavelet decomposition (like the output of pywt.wavedec2()).
Return type:	list of array_like

Notes

x, locations are the output of combine_chunks().

mr_utils.utils.wavelet.wavelet_forward(x, wavelet, mode='symmetric', level=None, axes=(-2, -1))[source]¶

Wrapper for the multilevel 2D discrete wavelet transform.

Parameters:

x (array_like) – Input data.
wavelet (str) – Wavelet to use.
mode (str, optional) – Signal extension mode.
level (int, optional) – Decomposition level (must be >= 0).
axes (tuple, optional) – Axes over which to compute the DWT.

Returns:

wavelet_transform (array_like) – The stitched together elements wvlt (see combine_chunks).
locations (list) – Indices telling us how we stitched it together so we can take it back apart.

Notes

See PyWavelets documentation on pywt.wavedec2() for more information.

If level=None (default) then it will be calculated using the dwt_max_level function.

mr_utils.utils.wavelet.wavelet_inverse(coeffs, locations, wavelet, mode='symmetric', axes=(-2, -1))[source]¶

Wrapper for the multilevel 2D inverse DWT.

Parameters:	coeffs (array_like) – Combined coefficients. locations (list) – Indices where the coefficients for each block are located. wavelet (str) – Wavelet to use. mode (str, optional) – Signal extension mode. axes (tuple, optional) – Axes over which to compute the IDWT.
Returns:	Inverse transform of wavelet transform, the original image.
Return type:	array_like

Notes

coeffs, locations are the output of forward().