Sparse along one dimension, 2D{1,1} dataset

The following is an example [1] of a 2D{1,1} sparse dataset with two-dimensions, \(d=2\), and two, \(p=2\), sparse single-component dependent-variables, where the component is sparsely sampled along one dimension. The following is an example of a hypercomplex acquisition of the NMR dataset.

Let’s import the CSD model data-file.

import csdmpy as cp

filename = "https://www.ssnmr.org/sites/default/files/CSDM/sparse/iglu_1d.csdf"
sparse_1d = cp.load(filename)

There are two linear dimensions and two single-component sparse dependent variables. The tuple of the dimension and the dependent variable instances are

x = sparse_1d.dimensions
y = sparse_1d.dependent_variables

The coordinates, viewed only for the first ten coordinates, are

print(x[0].coordinates[:10])

[   0.  192.  384.  576.  768.  960. 1152. 1344. 1536. 1728.] us

print(x[1].coordinates[:10])

[   0.  192.  384.  576.  768.  960. 1152. 1344. 1536. 1728.] us

Converting the coordinates to ms.

x[0].to("ms")
x[1].to("ms")

Visualizing the dataset

import matplotlib.pyplot as plt

# split the CSDM object with two dependent variables into two CSDM objects with single
# dependent variables.

cos, sin = sparse_1d.split()

# cosine data
plt.figure(figsize=(5, 3.5))
ax = plt.subplot(projection="csdm")
cb = ax.contourf(cos.real)
plt.colorbar(cb, ax=ax)
plt.tight_layout()
plt.show()

# sine data
plt.figure(figsize=(5, 3.5))
ax = plt.subplot(projection="csdm")
cb = ax.contourf(sin.real)
plt.colorbar(cb, ax=ax)
plt.tight_layout()
plt.show()

Citation

[1]

Balsgart NM, Vosegaard T., Fast Forward Maximum entropy reconstruction of sparsely sampled data., J Magn Reson. 2012, 223, 164-169. doi: 10.1016/j.jmr.2012.07.002