Linear operators

Abstraction of linear operators as matrices \(y = A*x\). The implementation follow the SigPy and LinearmapAA.

Common operators, including +, -, *, are overloaded. One may freely compose operators as long as the size matches.

New linear operators require to implement _apply (forward, \(A\)) and _adjoint (conjugate adjoint, \(A'\)) functions, as well as size. Recommendation for efficient backpropagation (but you do not have to do this if the AD is efficient enough):

class forward(torch.autograd.Function):
    @staticmethod
    def forward(ctx, data_in):
        return forward_func(data_in)
    @staticmethod
    def backward(ctx, grad_data_in):
        return adjoint_func(grad_data_in)
forward_op = forward.apply

class adjoint(torch.autograd.Function):
    @staticmethod
    def forward(ctx, data_in):
        return forward_func(data_in)
    @staticmethod
    def backward(ctx, grad_data_in):
        return adjoint_func(grad_data_in)
adjoint_op = adjoint.apply

mirtorch.linear.LinearMap.size_in: the size of the input of the linear map (a list)

mirtorch.linear.LinearMap.size_out: the size of the output of the linear map (a list)

Attributes of LinearMap

`mirtorch.linear.Add`	Addition of linear operators.
`mirtorch.linear.Multiply`	Scaling linear operators.
`mirtorch.linear.Matmul`	Matrix multiplication of linear operators.
`mirtorch.linear.ConjTranspose`	Hermitian transpose of linear operators.
`mirtorch.linear.Kron`	Create a LinearMap corresponding to the Kronecker product of a linear map with the identity matrix, i.e., kron(I_n, A), where A is a LinearMap.
`mirtorch.linear.BlockDiagonal`	Create a block-diagonal linear map from a list of linear maps.

Basic image processing operations

`mirtorch.linear.basics.Diffnd`	A multidimensional finite difference operator, with the periodic boundary condition.
`mirtorch.linear.basics.Diff2dgram`	A little more efficient way to implement the gram operator for the Gram (A'A) of finite difference.
`mirtorch.linear.basics.Diff3dgram`	A little more efficient way to implement the gram operator for the Gram of finite difference, with the reflexive boundary condition.
`mirtorch.linear.basics.Diag`	Expand an input vector into a diagonal matrix.
`mirtorch.linear.basics.Identity`	Identity mapping.
`mirtorch.linear.basics.Convolve1d`	1D cross-correlation linear map.
`mirtorch.linear.basics.Convolve2d`	2D cross-correlation linear map.
`mirtorch.linear.basics.Convolve3d`	3D cross-correlation linear map.
`mirtorch.linear.basics.Patch2D`	Patch operator to decompose image into blocks
`mirtorch.linear.basics.Patch3D`	Patch operator to decompose 3D image into patches.
`mirtorch.linear.wavelets.Wavelet2D`	A very preliminary implementation of 2D DWT.

MRI system models

`mirtorch.linear.mri.FFTCn`	FFT operators with FFTshift and iFFTshift for multidimensional data.
`mirtorch.linear.mri.NuSense`	Non-Cartesian sense operator: "SENSE: Sensitivity encoding for fast MRI" The implementation calls Matthew Muckley's Torchkbnufft toolbox: https://github.com/mmuckley/torchkbnufft The input/ourput size depends on the sensitivity maps.
`mirtorch.linear.mri.Sense`	Cartesian sense operator, following "SENSE: Sensitivity encoding for fast MRI".
`mirtorch.linear.mri.NuSenseGram`	Gram operator (A'A) of the Non-Cartesian sense operator: "SENSE: Sensitivity encoding for fast MRI" The implementation calls Matthew Muckley's Torchkbnufft toolbox: https://github.com/mmuckley/torchkbnufft The input/ourput size depends on the sensitivity maps.
`mirtorch.linear.mri.Gmri`	B0-informed mri reconstruction, the name follows MIRT.

SPECT system models

mirtorch.linear.spect.SPECT

Forward and back-projection methods for SPECT image reconstruction.

CT system models

mirtorch.linear.ct.Bdd

Forward and back-projection methods for CT image reconstruction.