GitHub

LinearOperatorCollection

Collection of linear operators for multi-dimensional signal and imaging tasks

Introduction

This package contains a collection of linear operators that are particularly useful for multi-dimensional signal and image processing tasks. Linear operators or linear maps behave like matrices in a matrix-vector product, but aren't necessarily matrices themselves. They can utilize more effective algorithms and can defer their computation until they are multiplied with a vector.

All operators provided by this package extend types and methods LinearOperators.jl. For example this package provides operators for the FFT (Fast Fourier Transform) and its non-equidistant variant (NFFT), the DCT (Discrete Cosine Transform), and the Wavelet transform. This package, however, does not implement these transformation itself but uses established libraries for them.

LinearOperatorCollection's main purpose is provide a wrapper around low-level libraries like FFTW.jl and NFFT.jl, which allows using the transformations as linear operators, i.e., implementing Op * x, adjoint(Op) * x and the mul! based in-place variants of the former.

Installation

Within Julia, use the package manager to install this package:

using Pkg
Pkg.add("LinearOperatorCollection")

This will install LinearOperatorCollection and a subset of the available operators. To keep the load time of this package low, many operators are implemented using package extensions. For instance, in order to get the FFTOp, one needs to install not only LinearOperatorCollection but also FFTW and load both in a Julia sessiong:

Pkg.add("FFTW")
using LinearOperatorCollection, FFTW

Small operators are implemented in LinearOperatorCollection directly.

License / Terms of Usage

The source code of this project is licensed under the MIT license. This implies that you are free to use, share, and adapt it. However, please give appropriate credit by citing the project.

Contact

If you have problems using the software, find mistakes, or have general questions please use the issue tracker to contact us.

There exist many related packages which also implement efficient and/or lazy operators:

Generally, it should be possible to combine operators and arrays from various packages.