dst1#

deepinv.physics.functional.dst1(x, *, dim=(-1,), inverse=False, orthosf=True)[source]#

Compute the one-dimensional discrete sine transform of type I (DST-I) or its inverse (IDST-I).

The DST-I of a vector \(x\) of length \(N\) is defined as

\[\mathrm{DST-I}(x)_k = - \frac{1}{2} \Im(\mathrm{DFT}(y_(k+1))),\]

where \(y\) is the odd extension of \(x\). The IDST-I is defined as

\[\mathrm{IDST-I}(x)_k = - \frac{1}{N + 1} \Im(\mathrm{DFT}(y_(k+1))).\]

If orthosf=True, it computes the orthogonal sign-flipped DST-I instead:

\[\mathrm{OSFDST-I}(x)_k = \frac{1}{\sqrt{2N + 2}} \Im(\mathrm{DFT}(y_(k+1))).\]

Note

The orthogonal sign-flipped DST-I is its own inverse, hence when orthosf=True, we have dst1(dst1(x)) = x and the parameter inverse has no effect.

Note

When multiple dimensions are specified, the DST-I is applied to each dimension separably.

Parameters:

x (torch.Tensor) – Input tensor.
dim (tuple) – Dimension along which to compute the transform. Default is (-1,) (the last dimension).
inverse (bool) – If True, compute the inverse DST-I (IDST-I). If False (default), compute the DST-I. It has not effect when ortho=True.
orthosf (bool) – If True (default), compute the orthogonal sign-flipped DST-I, otherwise compute the standard DST-I.

Returns:

(torch.Tensor) The transformed tensor.

Return type:

Tensor