tfmri.recon.adjoint

adjoint(kspace, image_shape, mask=None, trajectory=None, density=None, sensitivities=None, phase=None, sens_norm=True)[source]

Reconstructs an MR image using the adjoint MRI operator.

Given k-space data \(b\), this function estimates the corresponding image as \(x = A^H b\), where \(A\) is the MRI linear operator.

This operator supports Cartesian and non-Cartesian k-space data.

Additional density compensation and intensity correction steps are applied depending on the input arguments.

This operator supports batched inputs. All batch shapes should be broadcastable with each other.

This operator supports multicoil imaging. Coil combination is triggered when sensitivities is not None. If you have multiple coils but wish to reconstruct each coil separately, simply set sensitivities to None. The coil dimension will then be treated as a standard batch dimension (i.e., it becomes part of ...).

Parameters

  • kspace –

    A Tensor. The k-space samples. Must have type complex64 or complex128. kspace can be either Cartesian or non-Cartesian. A Cartesian kspace must have shape [..., num_coils, *image_shape], where ... are batch dimensions. A non-Cartesian kspace must have shape [..., num_coils, num_samples]. If not multicoil (sensitivities is None), then the num_coils axis must be omitted.

  • image_shape – A TensorShape or a list of ints. Must have length 2 or 3. The shape of the reconstructed image[s].

  • mask – An optional Tensor of type bool. The sampling mask. Must have shape [..., image_shape]. mask should be passed for reconstruction from undersampled Cartesian k-space. For each point, mask should be True if the corresponding k-space sample was measured and False otherwise.

  • trajectory – An optional Tensor of type float32 or float64. Must have shape [..., num_samples, rank]. trajectory should be passed for reconstruction from non-Cartesian k-space.

  • density –

    An optional Tensor of type float32 or float64. The sampling densities. Must have shape [..., num_samples]. This input is only relevant for non-Cartesian MRI reconstruction. If passed, the MRI linear operator will include sampling density compensation. If None, the MRI operator will not perform sampling density compensation.

  • sensitivities – An optional Tensor of type complex64 or complex128. The coil sensitivity maps. Must have shape [..., num_coils, *image_shape]. If provided, a multi-coil parallel imaging reconstruction will be performed.

  • phase – An optional Tensor of type float32 or float64. Must have shape [..., *image_shape]. A phase estimate for the reconstructed image. If provided, a phase-constrained reconstruction will be performed. This improves the conditioning of the reconstruction problem in applications where there is no interest in the phase data. However, artefacts may appear if an inaccurate phase estimate is passed.

  • sens_norm –

    A boolean. Whether to normalize coil sensitivities. Defaults to True.

Returns

A Tensor. The reconstructed image. Has the same type as kspace and shape [..., *image_shape], where ... is the broadcasted batch shape of all inputs.

Notes

Reconstructs an image by applying the adjoint MRI operator to the k-space data. This typically involves an inverse FFT or a (density-compensated) NUFFT, and coil combination for multicoil inputs. This type of reconstruction is often called zero-filled reconstruction, because missing k-space samples are assumed to be zero. Therefore, the resulting image is likely to display aliasing artefacts if k-space is not sufficiently sampled according to the Nyquist criterion.