mrpro.operators.PCACompressionOp

class mrpro.operators.PCACompressionOp(data: Tensor, n_components: int)

Bases: LinearOperator

PCA based compression operator.

__init__(data: Tensor, n_components: int)

Construct a PCA based compression operator.

The operator carries out an SVD followed by a threshold of the n_components largest values along the last dimension of a data with shape (*other, joint_dim, compression_dim). A single SVD is carried out for everything along joint_dim. Other are batch dimensions.

Consider combining this operator with mrpro.operators.RearrangeOp to make sure the data is in the correct shape before applying.

Parameters:

• data – Data of shape (*other, joint_dim, compression_dim) to be used to find the principal components.

• n_components – Number of principal components to keep along the compression_dim.

adjoint(data: Tensor) → tuple[Tensor]

Apply the adjoint compression to the data.

Parameters:

data – compressed data of shape (*other, joint_dim, n_components)

Return type:

expanded data of shape (*other, joint_dim, compression_dim)

forward(data: Tensor) → tuple[Tensor]

Apply the compression to the data.

Parameters:

data – data to be compressed of shape (*other, joint_dim, compression_dim)

Return type:

compressed data of shape (*other, joint_dim, n_components)

operator_norm(initial_value: Tensor, dim: Sequence[int] | None, max_iterations: int = 20, relative_tolerance: float = 0.0001, absolute_tolerance: float = 1e-05, callback: Callable[[Tensor], None] | None = None) → Tensor

Power iteration for computing the operator norm of the linear operator.

Parameters:

• initial_value – initial value to start the iteration; if the initial value contains a zero-vector for one of the considered problems, the function throws an value error.

• dim – the dimensions of the tensors on which the operator operates. For example, for a matrix-vector multiplication example, a batched matrix tensor with shape (4,30,80,160), input tensors of shape (4,30,160) to be multiplied, and dim = None, it is understood that the matrix representation of the operator corresponds to a block diagonal operator (with 4*30 matrices) and thus the algorithm returns a tensor of shape (1,1,1) containing one single value. In contrast, if for example, dim=(-1,), the algorithm computes a batched operator norm and returns a tensor of shape (4,30,1) corresponding to the operator norms of the respective matrices in the diagonal of the block-diagonal operator (if considered in matrix representation). In any case, the output of the algorithm has the same number of dimensions as the elements of the domain of the considered operator (whose dimensionality is implicitly defined by choosing dim), such that the pointwise multiplication of the operator norm and elements of the domain (to be for example used in a Landweber iteration) is well-defined.

• max_iterations – maximum number of iterations

• relative_tolerance – absolute tolerance for the change of the operator-norm at each iteration; if set to zero, the maximal number of iterations is the only stopping criterion used to stop the power iteration

• absolute_tolerance – absolute tolerance for the change of the operator-norm at each iteration; if set to zero, the maximal number of iterations is the only stopping criterion used to stop the power iteration

• callback – user-provided function to be called at each iteration

Return type:

an estimaton of the operator norm

property H: LinearOperator

Adjoint operator.

property gram: LinearOperator

Gram operator.

For a LinearOperator \(A\), the self-adjoint Gram operator is defined as \(A^H A\).

Note: This is a default implementation that can be overwritten by subclasses for more efficient implementations.