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Multichannel compressive sensing MRI using noiselet encoding.

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  • 1Department of Electrical and Computer System Engineering, Monash University, Melbourne, Australia; Indian Institute of Technology Bombay, Mumbai, India; IITB Monash Research Academy, Mumbai, India.

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This study introduces noiselet encoding for compressive sensing MRI, improving image quality and acceleration. Noiselet encoding enhances incoherence and the restricted isometry property, outperforming traditional Fourier methods in MRI scans.

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Area of Science:

  • Magnetic Resonance Imaging (MRI)
  • Signal Processing
  • Applied Mathematics

Background:

  • Compressive sensing MRI (CS-MRI) performance is limited by incoherence between measurement and sparsifying transforms, and the restricted isometry property (RIP) of the measurement matrix.
  • The standard CS-MRI approach uses an under-sampled Fourier matrix and wavelet transform, but their incoherence is suboptimal, impacting image reconstruction quality.

Purpose of the Study:

  • To improve CS-MRI performance by introducing noiselet unitary bases as the measurement matrix, enhancing incoherence and RIP.
  • To develop and evaluate a multichannel compressive sensing (MCS) framework leveraging multichannel MRI data acquisition.
  • To compare the performance of noiselet encoding versus Fourier encoding in MCS-MRI reconstructions.

Main Methods:

  • Introduced noiselet unitary bases as a measurement matrix to maximize incoherence with wavelet sparsifying transforms.
  • Developed a multichannel compressive sensing (MCS) framework for CS-MRI.
  • Conducted empirical RIP analysis comparing multichannel noiselet and Fourier measurement matrices.
  • Performed simulations comparing noiselet and Fourier encoding reconstructions at various acceleration factors.
  • Designed and implemented a tailored pulse sequence for noiselet domain data acquisition on a 3T scanner.

Main Results:

  • Noiselet measurement matrices demonstrated superior RIP compared to Fourier matrices in CS-MRI.
  • Noiselet-encoded MCS-MRI outperformed Fourier-encoded MCS-MRI in preserving image resolution.
  • Noiselet encoding enabled higher acceleration factors in CS-MRI.
  • Experimental data acquisition in the noiselet domain confirmed its feasibility and superior resolution preservation compared to Fourier encoding.

Conclusions:

  • Noiselet encoding offers a significant advantage over traditional Fourier encoding for CS-MRI.
  • The proposed MCS framework with noiselet encoding enhances image quality and allows for greater acceleration in MRI.
  • Noiselet encoding is a viable technique for improving the performance of compressive sensing MRI, with practical implementation demonstrated on a 3T scanner.