Matrix-Compression Techniques

Matrix compression can significantly accelerate the reconstruction process. This is achieved by transforming the system matrix S into a different domain through a basis transformation applied to its rows.

In MPIReco.jl, matrix compression can be enabled by specifying a sparse system-matrix loading parameter and selecting the desired sparsity transformation.

params = Dict{Symbol, Any}()
params[:SNRThresh] = 2
params[:frames] = 1:100
params[:numAverages] = 100
params[:minFreq] = 80e3
params[:recChannels] = 1:2
params[:iterations] = 3
params[:spectralLeakageCorrection] = false
params[:sf] = bSF;

We first reconstruct as usual:

cDense = reconstruct("SinglePatch", b; params...);

[ Info: Loading SM
[ Info: Preparing SF
[ Info: Adapting SF

Afterwards we use a blueprint with a sparse system-matrix loading and setting a sparsity transformation:

cSparse = reconstruct("SinglePatchSparse", b; params..., sparseTrafo = "FFT");

[ Info: compression factor = 0.0996900826446281 numCoeff = 193.0
[ Info: Preparing SF
[ Info: Adapting SF

Possible transformations are "FFT", "DCT_IV" and "DST".

The transformations can be restricted to the drive-field field-of-view by setting useDFFoV = true. The compression factor, which controls how many coefficients are dropped after applying the transformation, is determined by the redFactor parameter. For example, a reduction factor of redFactor = 0.01 will drop 99% of the data.

cRed = reconstruct("SinglePatchSparse", b; params..., sparseTrafo = "FFT", useDFFoV = true, redFactor = 0.01);

[ Info: compression factor = 0.00945179584120983 numCoeff = 5.0
[ Info: Preparing SF
[ Info: Adapting SF

We can again visualize the data with CairoMakie:

fig = Figure();
hidedecorations!(heatmap(fig[1, 1], cDense[1, :, :, 1, 1].data.data, axis = (title = "Dense",)).axis)
hidedecorations!(heatmap(fig[1, 2], cSparse[1, :, :, 1, 1].data.data, axis = (title = "Sparse",)).axis)
hidedecorations!(heatmap(fig[1, 3], cRed[1, :, :, 1, 1].data.data, axis = (title = "Sparse DF FOV",)).axis)
fig

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