Multi-Contrast Reconstruction

So far we have discussed single-contrast reconstructions of the form:

\[\begin{equation} \underset{\mathbf{c}}{argmin} \frac{1}{2}\vert\vert \mathbf{S}\mathbf{c}-\mathbf{u} \vert\vert_2^2 + + \mathbf{R(x)} \end{equation}\]

where $\mathbf{S}$ is a single system matrix, $\mathbf{u}$ is the measurement vector, and $\mathbf{R(x)}$ is an (optional) regularization term. In a multi-contrast reconstruction one can use two or more system matrices to solve:

\[\begin{equation} \underset{c1c2}{argmin} \frac{1}{2}\left\| \mathbf{S_1S_2} \begin{pmatrix} \mathbf{c_1} \\ \mathbf{c_2} \end{pmatrix} - \mathbf{u} \right\|_2^2 + \mathbf{R(x)} \end{equation}\]

To apply this technique to our algorithms, we simply have to provide multiple system matrices to our reconstructions:

bContrast = MultiContrastFile([bSF, bSF])

Multi Contrast File: MPIFile[MDFFile
	Study: "FocusField", Dates.DateTime("2014-11-13T16:20:01.217")
	Experiment: "SF_DF10_Middle (E39)", Dates.DateTime("2014-11-19T19:31:31.527")
, MDFFile
	Study: "FocusField", Dates.DateTime("2014-11-13T16:20:01.217")
	Experiment: "SF_DF10_Middle (E39)", Dates.DateTime("2014-11-19T19:31:31.527")
]

and can then reconstruct as usual:

c = reconstruct("SinglePatch", b;
                   SNRThresh=5,
                   sf = bContrast,
                   frames=1:acqNumFrames(b),
                   minFreq=80e3,
                   recChannels=1:rxNumChannels(b),
                   iterations=1,
                   spectralLeakageCorrection=true);
size(c)

(2, 32, 32, 1, 1)

Note that c now has two entries in its first dimension, one for each contrast.

We can then just simply access the data of each contrast by accessing the specific dimensions:

fig = Figure();
hidedecorations!(heatmap(fig[1, 1], c[1, :, :, 1, 1].data.data, axis = (title = "Contrast 1",)).axis)
hidedecorations!(heatmap(fig[1, 2], c[2, :, :, 1, 1].data.data, axis = (title = "Contrast 2",)).axis)
fig

In this case the channels are identical, because we reused the same system matrix.

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