scarlet.wavelet

exception scarlet.wavelet.InputError(message)

Bases: Exception

Exception raised for errors in the input.

Attributes:

expression – input expression in which the error occurred message – explanation of the error

class scarlet.wavelet.Starlet(image, coefficients, generation, convolve2D)

Bases: object

A class used to create the Wavelet transform of a cube of images from the ‘a trou’ algorithm.

The transform is performed by convolving the image by a seed starlet: the transform of an all-zero image with its central pixel set to one. This requires 2-fold padding of the image and an odd pad shape. The fft of the seed starlet is cached so that it can be reused in the transform of other images that have the same shape.

Attributes

coefficients

Starlet coefficients

convolve2D

Filter used to create starlet coefficients

generation

The generation of the starlet transform

image

The real space image

norm

The norm of a convolved dirac

scales

Number of starlet scales

Methods

from_coefficients(coefficients[, …])	Generate an image from a set of starlet coefficients
from_image(image[, scales, generation, …])	Generate a set of starlet coefficients for an image

property coefficients

Starlet coefficients

property convolve2D

Filter used to create starlet coefficients

static from_coefficients(coefficients, generation=2, convolve2D=None)

Generate an image from a set of starlet coefficients

Parameters

coefficients: array-like

The starlet coefficients used to generate the image

generation: int

The generation of the starlet transform (either 1 or 2).

convolve2D: array-like

The filter used to convolve the image and create the wavelets. When convolve2D is None this uses a cubic bspline.

Returns

result: Starlet

The resulting Starlet that contains the image, starlet coefficients, as well as the parameters used to generate the image.

static from_image(image, scales=None, generation=2, convolve2D=None)

Generate a set of starlet coefficients for an image

Parameters

image: array-like

The image that is converted into starlet coefficients

scales: int

The number of starlet scales to use. If scales is None then the maximum number of scales is used. Note: this is the length of the coefficients-1, as in the notation of Starck et al. 2011.

generation: int

The generation of the starlet transform (either 1 or 2).

convolve2D: array-like

The filter used to convolve the image and create the wavelets. When convolve2D is None this uses a cubic bspline.

Returns

result: Starlet

The resulting Starlet that contains the image, starlet coefficients, as well as the parameters used to generate the coefficients.

property generation

The generation of the starlet transform

property image

The real space image

property norm

The norm of a convolved dirac

property scales

Number of starlet scales

scarlet.wavelet.apply_wavelet_denoising(image, sigma=None, k=3, epsilon=0.1, max_iter=20, image_type='ground', positive=True)

Apply wavelet denoising

Uses the algorithm and notation from Starck et al. 2011, section 4.1

Parameters

image: array-like

The image to denoise

sigma: float

The standard deviation of the image

k: float

The threshold in units of sigma to declare a coefficient significant

epsilon: float

Convergence criteria for determining the support

max_iter: int

The maximum number of iterations. This applies to both finding the support and the denoising loop.

image_type: str

The type of image that is being used. This should be “ground” for ground based images with wide PSFs or “space” for images from space-based telescopes with a narrow PSF.

positive: bool

Whether or not the expected result should be positive

Returns

result: np.ndarray

The resulting denoised image after max_iter iterations.

scarlet.wavelet.get_multiresolution_support(image, starlets, sigma, K=3, epsilon=0.1, max_iter=20, image_type='ground')

Calculate the multi-resolution support for a dictionary of starlet coefficients

This is different for ground and space based telescopes. For space-based telescopes the procedure in Starck and Murtagh 1998 iteratively calculates the multi-resolution support. For ground based images, where the PSF is much wider and there are no pixels with no signal at all scales, we use a modified method that estimates support at each scale independently.

Parameters

image: 2D array

The image to transform into starlet coefficients.

starlets: array with dimension (scales+1, Ny, Nx)

The starlet dictionary used to reconstruct image.

sigma: float

The standard deviation of the image.

K: float

The multiple of sigma to use to calculate significance. Coefficients w where |w| > K*sigma_j, where sigma_j is standard deviation at the jth scale, are considered significant.

epsilon: float

The convergence criteria of the algorithm. Once |new_sigma_j - sigma_j|/new_sigma_j < epsilon the algorithm has completed.

max_iter: int

Maximum number of iterations to fit sigma_j at each scale.

image_type: str

The type of image that is being used. This should be “ground” for ground based images with wide PSFs or “space” for images from space-based telescopes with a narrow PSF.

Returns

M: array of int

Mask with significant coefficients in starlets set to True.

scarlet.wavelet.get_scales(image_shape, scales=None)

Get the number of scales to use in the starlet transform.

Parameters

image_shape: tuple

The 2D shape of the image that is being transformed

scales: int

The number of scale to transform with starlets. The total dimension of the starlet will have scales+1 dimensions, since it will also hold the image at all scales higher than scales.

scarlet.wavelet.starlet_reconstruction(starlets, generation=2, convolve2D=None)

Reconstruct an image from a dictionary of starlets

Parameters

starlets: array with dimension (scales+1, Ny, Nx)

The starlet dictionary used to reconstruct the image.

convolve2D: function

The filter function to use to convolve the image with starlets in 2D.

Returns

image: 2D array

The image reconstructed from the input starlet.

scarlet.wavelet.starlet_transform(image, scales=None, generation=2, convolve2D=None)

Perform a scarlet transform, or 2nd gen starlet transform.

Parameters

image: 2D array

The image to transform into starlet coefficients.

scales: int

The number of scale to transform with starlets. The total dimension of the starlet will have scales+1 dimensions, since it will also hold the image at all scales higher than scales.

generation: int

The generation of the transform. This must be 1 or 2.

convolve2D: function

The filter function to use to convolve the image with starlets in 2D.

Returns

starlet: array with dimension (scales+1, Ny, Nx)

The starlet dictionary for the input image.