tfmri.linalg.LinearOperatorGramMRI

class LinearOperatorGramMRI(image_shape, extra_shape=None, mask=None, trajectory=None, density=None, sensitivities=None, phase=None, fft_norm='ortho', sens_norm=True, dynamic_domain=None, toeplitz_nufft=False, dtype=tf.complex64, name='LinearOperatorGramMRI')[source]

Bases: tensorflow_mri.python.ops.linalg_ops.LinearOperatorMRI

Linear operator representing an MRI encoding matrix.

If \(A\) is a tfmri.linalg.LinearOperatorMRI, then this ooperator represents the matrix \(G = A^H A\).

In certain circumstances, this operator may be able to apply the matrix \(G\) more efficiently than the composition \(G = A^H A\) using tfmri.linalg.LinearOperatorMRI objects.

Parameters

  • image_shape – A tf.TensorShape or a list of ints. The shape of the images that this operator acts on. Must have length 2 or 3.

  • extra_shape –

    An optional tf.TensorShape or list of ints. Additional dimensions that should be included within the operator domain. Note that extra_shape is not needed to reconstruct independent batches of images. However, it is useful when this operator is used as part of a reconstruction that performs computation along non-spatial dimensions, e.g. for temporal regularization. Defaults to None.

  • mask – An optional tf.Tensor of type tf.bool. The sampling mask. Must have shape [..., *S], where S is the image_shape and ... is the batch shape, which can have any number of dimensions. If mask is passed, this operator represents an undersampled MRI operator.

  • trajectory –

    An optional tf.Tensor of type float32 or float64. Must have shape [..., M, N], where N is the rank (number of spatial dimensions), M is the number of samples in the encoded space and ... is the batch shape, which can have any number of dimensions. If trajectory is passed, this operator represents a non-Cartesian MRI operator.

  • density –

    An optional tf.Tensor of type float32 or float64. The sampling densities. Must have shape [..., M], where M is the number of samples and ... is the batch shape, which can have any number of dimensions. This input is only relevant for non-Cartesian MRI operators. If passed, the non-Cartesian operator will include sampling density compensation. If None, the operator will not perform sampling density compensation.

  • sensitivities –

    An optional tf.Tensor of type complex64 or complex128. The coil sensitivity maps. Must have shape [..., C, *S], where S is the image_shape, C is the number of coils and ... is the batch shape, which can have any number of dimensions.

  • phase –

    An optional tf.Tensor of type float32 or float64. A phase estimate for the image. If provided, this operator will be phase-constrained.

  • fft_norm –

    FFT normalization mode. Must be None (no normalization) or 'ortho'. Defaults to 'ortho'.

  • sens_norm – A boolean. Whether to normalize coil sensitivities. Defaults to True.

  • dynamic_domain – A str. The domain of the dynamic dimension, if present. Must be one of 'time' or 'frequency'. May only be provided together with a non-scalar extra_shape. The dynamic dimension is the last dimension of extra_shape. The 'time' mode (default) should be used for regular dynamic reconstruction. The 'frequency' mode should be used for reconstruction in x-f space.

  • toeplitz_nufft –

    A boolean. If True, uses the Toeplitz approach [5] to compute \(F^H F x\), where \(F\) is the non-uniform Fourier operator. If False, the same operation is performed using the standard NUFFT operation. The Toeplitz approach might be faster than the direct approach but is slightly less accurate. This argument is only relevant for non-Cartesian reconstruction and will be ignored for Cartesian problems.

  • dtype – A tf.dtypes.DType. The dtype of this operator. Must be complex64 or complex128. Defaults to complex64.

  • name –

    An optional str. The name of this operator.

Initialize the LinearOperator. (deprecated arguments)

Deprecated: SOME ARGUMENTS ARE DEPRECATED: (graph_parents). They will be removed in a future version. Instructions for updating: Do not pass graph_parents. They will no longer be used.

This is a private method for subclass use. Subclasses should copy-paste this ``__init__`` documentation.

Parameters

  • dtype – The type of the this LinearOperator. Arguments to matmul and solve will have to be this type.

  • graph_parents – (Deprecated) Python list of graph prerequisites of this LinearOperator Typically tensors that are passed during initialization

  • is_non_singular – Expect that this operator is non-singular.

  • is_self_adjoint – Expect that this operator is equal to its hermitian transpose. If dtype is real, this is equivalent to being symmetric.

  • is_positive_definite – Expect that this operator is positive definite, meaning the quadratic form x^H A x has positive real part for all nonzero x. Note that we do not require the operator to be self-adjoint to be positive-definite. See: https://en.wikipedia.org/wiki/Positive-definite_matrix#Extension_for_non-symmetric_matrices

  • is_square – Expect that this operator acts like square [batch] matrices.

  • name – A name for this LinearOperator.

  • parameters – Python dict of parameters used to instantiate this LinearOperator.

Raises

  • ValueError –

    If any member of graph_parents is None or not a Tensor.

  • ValueError – If hints are set incorrectly.