truncate_rank¶

Rank truncation filter via truncated SVD reconstruction. Reconstructs the input using only singular vectors start through stop, removing all other components. In high frame rate ultrasound (Doppler, flow imaging), the first singular components capture stationary tissue clutter. Removing them isolates the weaker blood flow signal.

The input is internally reshaped to a 2D matrix \((m, n)\) where \(m\) is the size of the first dimension (the frame axis) and \(n\) is the product of all remaining dimensions (spatial). The SVD is computed on this matrix, and the output is reconstructed from the selected singular components.

Signature¶

PythonMATLAB

ffdas.truncate_rank(
    x,
    start,
    stop=None,
    *,
    out=None,
)

y = ffdas.truncate_rank(x, start)
y = ffdas.truncate_rank(x, start, stop)

Parameters¶

Parameter	Python	MATLAB	Description
`x`	at least 2D	at least 2D	Input array. The first dimension (Python) or last dimension (MATLAB) is the frame axis.
`start`	`int`, 0-based	`int`, 1-based	Index of the first singular vector to keep.
`stop`	`int` or `None`	`int` or `[]`	Index past the last singular vector to keep (exclusive in Python, inclusive in MATLAB). Defaults to \(\min(m, n)\).

Returns¶

Filtered array with the same shape and dtype as the input.

Example¶

In high frame rate ultrasound imaging, the first few singular components typically capture stationary tissue (high energy, low rank). Setting start to skip these isolates the weaker flow signal.

PythonMATLAB

# volumes: (n_frames, nz, ny, nx)
# tissue is approximately rank 1; skip the first singular vector
flow = ffdas.truncate_rank(volumes, start=1)

# keep only components 5 through 20
band = ffdas.truncate_rank(volumes, start=5, stop=20)

% volumes: (nz, ny, nx, n_frames)
% skip the first singular vector (1-based)
flow = ffdas.truncate_rank(volumes, 2);

% keep components 6 through 20
band = ffdas.truncate_rank(volumes, 6, 20);

Notes¶

The implementation uses cuSOLVER for the SVD computation.