**tl;dr** An exploration of compressed sensing fMRI time series with 3 different algorithms. Typically, compressed sensing reconstructs a single volume of MRI but fMRI are composed of many volumes; sensing along the time domain could reduce the number of volumes required. Of the 3 algorithms, BSBL-BO performed the best with the error curve elbowing around 30% subsampling.

# Links

# Abstract

Compressed sensing reconstructs signals by solving underdetermined linear systems under the con- ditions that the measurements are sparse in the domain and incoherent [1]. In engineering, if measurements are taken within an appropriate basis satisfying the restricted isometry property, i.e., the Gaussian, Bernoulli, or Fourier bases, then this prior structure makes full signal recovery possible [2].

Compressed sensing is challenging with fMRI because the temporal dynamics of hemodynamic signals are relatively slow compared to other fast-acquisition signals that historically benefit from compressed sensing [3]. Additionally, having fewer samples insinuates a loss of statistical power in subsequent analyses. Thankfully, fMRI signals boast two beneficial characteristics that are promising for compressed sensing: 1. they are linear time-invariant, and 2. they lie within, and can transformed by, a Fourier basis [4].

In medical imaging, it is often assumed that an image is sampled at the Nyquist rate, s.t., enough discrete measurements are taken to reconstruct a continuous whole (M > N) without loss of information. If high-fidelity reconstruction is possible sampling below the Nyquist rate, then MRI modalities would benefit since discerning a signal and quickly turning over an analysis reduces real costs. These potential gains beg the question: if an underdetermined linear system can be solved after sampling below the Nyquist rate, can we collect fewer samples and still recover a high-quality fMRI under a compressed sensing paradigm? The purpose of this project is to explore approaches to compressed sensing that yield meaningful signal recoveries from heavy undersampling.

# Results

# References

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