Linear Operators (sigpy.linop)

This module contains an abstraction class Linop for linear operators, and provides commonly used linear operators, including signal transforms such as FFT, NUFFT, and wavelet, and array manipulation operators, such as reshape, transpose, and resize.

The Linear Operator Class

sigpy.linop.Linop

Abstraction for linear operator.

Linop Manipulation

The following are classes that take in Linops and compose them to form a new Linop.

sigpy.linop.Conj	Complex conjugate of linear operator.
sigpy.linop.Add	Addition of linear operators.
sigpy.linop.Compose	Composition of linear operators.
sigpy.linop.Hstack	Horizontally stack linear operators.
sigpy.linop.Vstack	Vertically stack linear operators.
sigpy.linop.Diag	Diagonally stack linear operators.

Basic Linops

sigpy.linop.Embed	Embed input into a zero array with the given shape and index.
sigpy.linop.Identity	Identity linear operator.
sigpy.linop.Reshape	Reshape input to given output shape.
sigpy.linop.Slice	Slice input with given index.
sigpy.linop.Transpose	Tranpose input with the given axes.

Computing Related Linops

sigpy.linop.ToDevice	Move input between devices.
sigpy.linop.AllReduce	Performs all reduce between MPI ranks.
sigpy.linop.AllReduceAdjoint	All reduce adjoint operator.

Convolution Linops

sigpy.linop.ConvolveData	Convolution operator for data arrays.
sigpy.linop.ConvolveDataAdjoint	Adjoint convolution operator for data arrays.
sigpy.linop.ConvolveFilter	Convolution operator for filter arrays.
sigpy.linop.ConvolveFilterAdjoint	Adjoint convolution operator for filter arrays.

Fourier Linops

sigpy.linop.FFT	FFT linear operator.
sigpy.linop.IFFT	IFFT linear operator.
sigpy.linop.NUFFT	NUFFT linear operator.
sigpy.linop.NUFFTAdjoint	NUFFT adjoint linear operator.

Multiplication Linops

sigpy.linop.MatMul	Matrix multiplication.
sigpy.linop.RightMatMul	Matrix multiplication on the right.
sigpy.linop.Multiply	Multiplication linear operator.

Interapolation Linops

sigpy.linop.Interpolate	Interpolation linear operator.
sigpy.linop.Gridding	Gridding linear operator.

Array Manipulation Linops

sigpy.linop.Resize	Resize linear operator.
sigpy.linop.Flip	Flip linear operator.
sigpy.linop.Downsample	Downsampling linear operator.
sigpy.linop.Upsample	Upsampling linear operator.
sigpy.linop.Circshift	Circular shift linear operator.
sigpy.linop.Sum	Sum linear operator.
sigpy.linop.Tile	Tile linear operator.
sigpy.linop.FiniteDifference	Linear operator that computes finite difference gradient.

Wavelet Transform Linops

sigpy.linop.Wavelet	Wavelet transform linear operator.
sigpy.linop.InverseWavelet	Inverse wavelet transform linear operator.

Block Reshape Linops

sigpy.linop.ArrayToBlocks	Extract blocks from an array in a sliding window manner.
sigpy.linop.BlocksToArray	Accumulate blocks into an array in a sliding window manner.