Examples

PGURE-SVT can be used either from Python, or as a standalone executable.

The Python examples require the HyperSpy multi-dimensional data analysis toolbox to be installed. This provides a number of useful features including data visualization and data import from a number of microscopy file formats. To install it in a conda environment:

conda install hyperspy -c conda-forge

An example Jupyter notebook for both of these examples is provided here.

Simulated dataset

The first step is to load the simulated dataset from the examples/ directory using HyperSpy.

import numpy as np
import hyperspy.api as hs

from pguresvt import hspy, mixed_noise_model

# Load example dataset
s = hs.load("examples/example.tif")

# Truncate to 25 frames
s = s.inav[:25]

# Plot the result
s.plot(navigator='slider')

Now we corrupt the dataset with using a noise generator for mixed Poisson-Gaussian noise, according to the following equation, where the true, noise-free signal is \(\mathbf{X}_{0}\), and the observed noisy signal is \(\mathbf{Y}\).

\[\begin{split}\mathbf{Y}=\alpha\mathbf{Z}+\mathbf{E}\;\textrm{ with }\;\begin{cases} \mathbf{Z}\thicksim\mathcal{P}\left(\frac{\mathbf{X}^{0}}{\alpha}\right)\\ \mathbf{E}\thicksim\mathcal{N}\left(\mu,\sigma^{2}\right) \end{cases}\end{split}\]

where \(\alpha\) is the detector gain, \(\mu\) is the detector offset, and \(\sigma\) is the (Gaussian) detector noise.

random_seed = 123
detector_gain = 0.1
detector_offset = 0.1
detector_sigma = 0.1

noisy_data = mixed_noise_model(
    s.data,
    alpha=detector_gain,
    mu=detector_offset,
    sigma=detector_sigma,
    random_seed=random_seed,
)

s_noisy = hs.signals.Signal2D(noisy_data)

# Plot the noisy result
s_noisy.plot(navigator="slider")

In this example we do not use the noise estimation procedure, and instead provide the known parameters to the algorithm directly. This information is used by the PGURE optimizer to calculate the appropriate threshold.

svt = hspy.HSPYSVT(
    patch_size=4,
    noise_alpha=detector_gain,
    noise_mu=detector_offset,
    noise_sigma=detector_sigma,
    tol=1e-5,
)

# Note that the denoising can take a few moments
s_denoised = svt.denoise(s_noisy)

# Plot the denoised result
s_denoised.plot(navigator='slider')

Nanoparticle dataset

In this example we apply PGURE-SVT to an experimental dataset of a nanoparticle acquired using ADF-STEM. This image sequence contains 50 frames at a rate of 4 frames per second. The results of this denoising are shown in Fig. 11 of the paper.

For larger images, such as the 256x256 pixels here, you can use the patch_overlap parameter to control the trade-off between speed and accuracy of the denoising procedure. This reduces the number of patches the algorithm works with, at the expense of introducing possible edge artefacts between patches.

For the experimental sequence, the detector offset (noise_mu) was known beforehand, so a noise estimation procedure is used for the other values.

# Load example dataset and plot
s_np = hs.load("nanoparticle.tif")
s_np.plot(navigator="slider")

# Initialize with suggested parameters, optimized for speed
expt_svt = hspy.HSPYSVT(patch_size=4, patch_overlap=2, noise_mu=0.075)

# Run the denoising
s_np_denoised = expt_svt.denoise(s_np)

# Plot denoised data
s_np_denoised.plot(navigator="slider")

Standalone executable

The PGURE-SVT standalone executable uses a simple command-line interface along with a separate parameter file.

./PGURE-SVT param.svt

Warning

The standalone executable currently only supports 8-bit and 16-bit TIFF sequences.

An example file, examples/param.svt is provided.

# Example parameter file for PGURE-SVT program

# Specify the file name of the TIFF stack to be denoised
filename             : ../test/examplesequence.tif

# The start and end frames of the sequence to be denoised
start_image          : 1
end_image            : 50