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.. _sphx_glr_auto_experiments_commonline_lud_simulated_data.py:


Commonlines Method using LUD
============================

This tutorial demonstrates using the Least Unsquared Deviations (LUD)
commonlines method for estimating particle orientations. This tutorial
reproduces the "Experiments on simulated images" found in the publication:

Orientation Determination of Cryo-EM Images Using Least Unsquared Deviations,
L. Wang, A. Singer, and  Z. Wen, SIAM J. Imaging Sciences, 6, 2450-2483 (2013).

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Imports
-------

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.. code-block:: Python


    import logging
    from fractions import Fraction
    from itertools import product

    import numpy as np

    from aspire.abinitio import CommonlineIRLS, CommonlineLUD
    from aspire.noise import WhiteNoiseAdder
    from aspire.source import Simulation
    from aspire.utils import mean_aligned_angular_distance
    from aspire.volume import Volume

    logger = logging.getLogger(__name__)



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Parameters
----------
Set up some initializing parameters. We will run the LUD algorithm using ADMM
and IRLS methods under various spectral norm constraints and levels of noise.

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.. code-block:: Python


    SNR = ["1/8", "1/16", "1/32"]  # Signal-to-noise ratio
    METHOD = ["ADMM", "IRLS"]
    ALPHA = [0.90, 0.75, 0.67]  # Spectral norm constraint
    n_imgs = 500  # Number of images in our source
    dtype = np.float64
    pad_size = 129


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Load Volume Map
---------------
We will generate simulated noisy images from a low res volume
map available in our data folder. This volume map is a 65 x 65 x 65
voxel volume which we intend to upsample to 129 x 129 x 129.
To do this we use our ``downsample`` method which, when provided a voxel
size larger than the input volume, internally zero-pads in Fourier
space to increase the overall shape of the volume.

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.. code-block:: Python

    vol = (
        Volume.load("../tutorials/data/clean70SRibosome_vol_65p.mrc")
        .astype(dtype)
        .downsample(pad_size)
    )
    logger.info("Volume map data" f" shape: {vol.shape} dtype:{vol.dtype}")


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Generate Noisy Images and Estimate Rotations
--------------------------------------------
A ``Simulation`` object is used to generate simulated data at various
noise levels. Then rotations are estimated using the ``CommonlineLUD`` and
``CommonlineIRLS`` algorithms. Results are measured by computing the mean
aligned angular distance between the ground truth rotations and the globally
aligned estimated rotations.

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.. code-block:: Python


    # Build table to dislay results.
    col_width = 21
    table = []
    table.append(
        f"{'METHOD':<{col_width}} {'SNR':<{col_width}} {'ALPHA':<{col_width}} {'Mean Angular Distance':<{col_width}}"
    )
    table.append("-" * (col_width * 4))

    for method, snr, alpha in product(METHOD, SNR, ALPHA):
        # Generate a white noise adder with specified SNR.
        noise_adder = WhiteNoiseAdder.from_snr(snr=Fraction(snr))

        # Initialize a Simulation source to generate noisy, centered images.
        src = Simulation(
            n=n_imgs,
            vols=vol,
            offsets=0,
            amplitudes=1,
            noise_adder=noise_adder,
            dtype=dtype,
        ).cache()

        # Estimate rotations using the LUD algorithm.
        if method == "ADMM":
            orient_est = CommonlineLUD(src, alpha=alpha)
        else:
            orient_est = CommonlineIRLS(src, alpha=alpha)
        est_rotations = orient_est.estimate_rotations()

        # Find the mean aligned angular distance between estimates and ground truth rotations.
        mean_ang_dist = mean_aligned_angular_distance(est_rotations, src.rotations)

        # Append results to table.
        table.append(
            f"{method:<{col_width}} {snr:<{col_width}} {str(alpha):<{col_width}} {mean_ang_dist:<{col_width}}"
        )


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Display Results
---------------
Display table of results for both methods using various spectral norm
constraints and noise levels.

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.. code-block:: Python


    logger.info("\n" + "\n".join(table))


.. _sphx_glr_download_auto_experiments_commonline_lud_simulated_data.py:

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      :download:`Download Python source code: commonline_lud_simulated_data.py <commonline_lud_simulated_data.py>`

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