Author: Samuel Farrens
Year: 2017
Version: 3.2
Email: samuel.farrens@gmail.com
Website: sfarrens.github.io
Reference Paper: arXiv:1703.02305

1. Introduction
2. Dependencies
3. Execution
   1. Input Format
   2. Running the executable script
   3. Running the code in a Python session
   4. Example
   5. Code Options
4. Troubleshooting

This repository contains a Python code designed for PSF deconvolution and analysis.

The directory lib contains all of the primary functions and classes used for optimisation and analysis. functions contains some additional generic functions and tools.

In order to run the code in this repository the following packages must be installed:

• Python 2.7 [Tested with v 2.7.11]

• Numpy [Tested with v 1.11.3]

• Scipy [Tested with v 0.18.1]

• Astropy [Tested with v 1.1.2]

• Matplotlib [Tested with v 1.5.3]

• Termcolor [Tested with v 1.1.0]

• The current implementation of wavelet transformations additionally requires the mr_transform.cc C++ script from the Sparse2D library in the iSap package [Tested with v 3.1]. These C++ scripts will be need to be compiled in order to run (see iSap Documentation for details).

The low-rank approximation method can be run purely in Python.

The primary code is an executable script called sf_deconvolve.py which is designed to take an observed (i.e. with PSF effects and noise) stack of galaxy images and a known PSF, and attempt to reconstruct the original images. The input format are Numpy binary files (.npy) or FITS image files (.fits).

The input files should have the following format:

• Input Images: This should be either a Numpy binary or a FITS file containing a 3D array of galaxy images. e.g. for a sample of 10 images, each with size 41x41, the shape of the array should be [10, 41, 41].

• Input PSF(s): This should be either a Numpy binary or a FITS file containing a 2D array (for a fixed PSF) or a 3D array (for a spatially varying PSF) of PSF images. For the spatially varying case the number of PSF images must match the number of corresponding galaxy images. e.g. For a sample of 10 images the codes expects 10 PSFs.

See the files provides in the examples directory for reference.

The code can be run in a terminal (not in a Python session) as follows:

$ sf_deconvolve.py -i INPUT_IMAGES.npy -p PSF.npy -o OUTPUT_NAME

Where INPUT_IMAGES.npy denotes the Numpy binary file containing the stack of observed galaxy images, PSF.npy denotes the PSF corresponding to each galaxy image and OUTPUT_NAME specifies the output path and file name.

Alternatively the code arguments can be stored in a configuration file (with any name) and the code can be run by providing the file name preceded by a @.

$ sf_deconvolve.py @config.ini

To run the code in an active Python session you should include the following imports:

>>> from lib.deconvolve import run
>>> from functions.log import set_up_log

Note: At present it is necessary to create a logging session but this may be relaxed in a future update.

The code can then be run as follows:

>>> log = set_up_log('LOG_FILE_NAME')
>>> primal_res, dual_res = run(INPUT_IMAGES, INPUT_PSFS, log=log, **KEYWORDS)

Where INPUT_IMAGES and INPUT_PSFS are both Numpy arrays and KEYWORDS is a dictionary that contains all of the parameter settings (this requires defining values for virtually all of the arguments listed below). The resulting deconvolved images will be saved to the variable primal_res.

The following example can be run on the sample data provided in the example directory.

This example takes a sample of 100 galaxy images (with PSF effects and added noise) and the corresponding PSFs, and recovers the original images using low-rank approximation via Condat-Vu optimisation.

$ sf_deconvolve.py -i example_image_stack.npy -p example_psf.npy -o example_output --mode lowr

The example can also be run using the configuration file provided.

The result will be two Numpy binary files called example_output_primal.npy and example_output_dual.npy corresponding to the primal and dual variables in the splitting algorithm. The reconstructed images will be in the example_output_primal.npy file.

The example can also be run with the FITS files provided.

• -i INPUT, --input INPUT: Input data file name. File should be a Numpy binary containing a stack of noisy galaxy images with PSF effects (i.e. a 3D array).

• -p PSF, --psf PSF: PSF file name. File should be a Numpy binary containing either: (a) a single PSF (i.e. a 2D array for fixed format) or (b) a stack of PSFs corresponding to each of the galaxy images (i.e. a 3D array for obj_var format).

• -h, --help: Show the help message and exit.

• -v, --version: Show the program's version number and exit.

• -q, --quiet: Suppress verbose for each iteration.

• -o, --output: Output file name. If not specified output files will placed in input file path.

• --output_format Output file format [npy or fits].

Initialisation:

• -k, --current_res: Current deconvolution results file name (i.e. the file containing the primal results from a previous run).

• --noise_est: Initial estimate of the noise standard deviation in the observed galaxy images. If not specified this quantity is automatically calculated using the median absolute deviation of the input image(s).

Optimisation:

• -m, --mode {all,sparse,lowr,grad}: Option to specify the optimisation mode [all, sparse, lowr or grad]. all performs optimisation using both low-rank approximation and sparsity, sparse using only sparsity, lowr uses only low-rank and grad uses only gradient descent. (default: lowr)

• --opt_type {condat,fwbw,gfwbw}: Option to specify the optimisation method to be implemented [condat, fwbw or gfwbw]. condat implements the Condat-Vu proximal splitting method, fwbw implements Forward-Backward splitting with FISTA speed-up and gfwbw implements the generalised Forward-Backward splitting method. (default: condat)

• --n_iter: Number of iterations. (default: 150)

• --cost_window: Window to measure cost function (i.e. interval of iterations for which cost should be calculated). (default: 1)

• --convergence: Convergence tolerance. (default: 0.0001)

• --no_pos: Option to turn off positivity constraint.

• --no_grad: Option to turn off gradient calculation.

Low-Rank Aproximation:

• --lowr_thresh_factor: Low rank threshold factor. (default: 1)

• --lowr_type: Type of low-rank regularisation [standard or ngole]. (default: standard)

• --lowr_thresh_type: Low rank threshold type [soft or hard]. (default: hard)

Sparsity:

• --wavelet_type: Type of Wavelet to be used (see iSap Documentation). (default: 1)

• --wave_thresh_factor: Wavelet threshold factor. (default: [3.0, 3.0, 4.0])

• --n_reweights: Number of reweightings. (default: 1)

Condat Algorithm:

• --relax: Relaxation parameter (rho_n in Condat-Vu method). (default: 0.8)

• --condat_sigma: Condat proximal dual parameter. (default: 0.5)

• --condat_tau: Condat proximal primal parameter. (default: 0.5)

Testing:

• -c, --clean_data: Clean data file name.

• -r, --random_seed: Random seed. Use this option if the input data is a randomly selected subset (with known seed) of the full sample of clean data.

• --kernel: Standard deviation of pixels for Gaussian kernel. This option will multiply the deconvolution results by a Gaussian kernel.

• --metric: Metric to average errors [median or mean]. (default: median)

• If you get the following error:

ERROR: svd() got an unexpected keyword argument 'lapack_driver'

Update your Numpy and Scipy installations

$ pip install --upgrade numpy
$ pip install --upgrade scipy