scarlet.fft¶

class scarlet.fft.Fourier(image, image_fft=None)[source]¶

Bases: object

An array that stores its Fourier Transform

The Fourier class is used for images that will make use of their Fourier Transform multiple times. In order to prevent numerical artifacts the same image convolved with different images might require different padding, so the FFT for each different shape is stored in a dictionary.

Attributes:

image: The real space image
shape: The shape of the real space image

Methods

`fft`(fft_shape, axes)	The FFT of an image for a given fft_shape along desired axes
`from_fft`(image_fft, fft_shape, image_shape)	Generate a new Fourier object from an FFT dictionary

fft(fft_shape, axes)[source]¶: The FFT of an image for a given fft_shape along desired axes

static from_fft(image_fft, fft_shape, image_shape, axes=None)[source]¶

Generate a new Fourier object from an FFT dictionary

If the fft of an image has been generated but not its real space image (for example when creating a convolution kernel), this method can be called to create a new Fourier instance from the k-space representation.

Parameters:

image_fft: array: The FFT of the image.
fft_shape: tuple: “Fast” shape of the image used to generate the FFT. This will be different than image_fft.shape if any of the dimensions are odd, since np.fft.rfft requires an even number of dimensions (for symmetry), so this tells np.fft.irfft how to go from complex k-space to real space.
image_shape: tuple: The shape of the image before padding. This will regenerate the image with the extra padding stripped.
axes: int or tuple: The dimension(s) of the array that will be transformed.

Returns:

result: Fourier: A Fourier object generated from the FFT.

property image¶: The real space image

property shape¶: The shape of the real space image

scarlet.fft.convolve(image, kernel, padding=3, axes=(-2, -1), return_Fourier=True)[source]¶

Convolve image with a kernel

Parameters:

image: array or `Fourier`: Image either as array or as Fourier object
kernel: array or `Fourier`: Convolution kernel either as array or as Fourier object
padding: int: Additional padding to use when generating the FFT to supress artifacts.
axes: tuple or None: Axes that contain the spatial information for the PSFs.
return_Fourier: bool: Whether to return Fourier or array

scarlet.fft.match_psf(psf1, psf2, padding=3, axes=(-2, -1), return_Fourier=True)[source]¶

Calculate the difference kernel to match psf1 to psf2

Parameters:

psf1: array or `Fourier`: PSF1 either as array or as Fourier object
psf2: array or `Fourier`: PSF1 either as array or as Fourier object
padding: int: Additional padding to use when generating the FFT to supress artifacts.
axes: tuple or None: Axes that contain the spatial information for the PSFs.
return_Fourier: bool: Whether to return Fourier or array

scarlet.fft.shift(image, shift, fft_shape=None, axes=(-2, -1), return_Fourier=True)[source]¶