lenspack.image.transforms module¶

lenspack.image.transforms.starlet2d(image, nscales=5)[source]¶

Compute the multiscale 2D starlet transform of an image.

Parameters

image (array_like (2D)) – Input image.
nscales (int) – Number of wavelet scales to compute. Should not exceed log2(N), where N is the smaller of the two input dimensions.

Returns

Wavelet coefficients. An input image of shape (N, M) and nscales equal to n will produce an output of shape (n + 1, N, M). The first n maps are wavelet coefficients, while the final map is the coarse scale map.

Return type

3D numpy array

Notes

This function produces the same output as the mr_transform binary of the Sparse2D C++ code package (see References) to high precision.

References

Starck, Murtagh, Fadili, ‘Sparse Image and Signal Processing: Wavelets and Related Geometric Multiscale Analysis’, Cambridge University Press, Cambridge (GB), 2016.
https://github.com/cosmostat/sparse2d

Examples

>>> # Transform a Gaussian random field of standard deviation 10.
>>> img = 10 * np.random.randn(64, 64)
>>> wt = starlet2d(img, 5)
>>> wt.shape
(6, 64, 64)

>>> # Reconstruction
>>> rec = np.sum(wt, axis=0)
>>> rec.shape == img.shape
True
>>> np.sum(np.abs(rec - img))
2.4814638191483773e-12

lenspack.image.transforms.dct2d(image, norm='ortho')[source]¶

Compute the discrete cosine transform (type 2) of an image.

Parameters

image (array_like, 2D) – Input image.
norm ({None, 'ortho', 'sparse2d'}, optional) – Normalization option. See scipy.fftpack.dct documentation (Type II) for a description of the None and ‘ortho’ options. The ‘sparse2d’ option is available to match the output from the im_dct Sparse2D binary, which involves an additional scaling of the zero-frequency elements. Default is ‘ortho’.

Returns

Type 2 DCT.

Return type

2D numpy array

Notes

Using no normalization (i.e. norm=None) will not automatically recover the original image after performing the inverse transformation. Each transform brings an overall scaling factor of 2N.