Compressed-Sensing MRI With Random Encoding

Abstract

Compressed sensing (CS) has the potential to reduce magnetic resonance (MR) data acquisition time. In order for CS-based imaging schemes to be effective, the signal of interest should be sparse or compressible in a known representation, and the measurement scheme should have good mathematical properties with respect to this representation. While MRimages are often compressible, the second requirement is often only weakly satisfied with respect to commonly used Fourier encoding schemes. This paper investigates the use of random encoding for CS-MRI, in an effort to emulate the “universal” encoding schemes suggested by the theoretical CS literature. This random encoding is achieved experimentally with tailored spatially-selective radio-frequency (RF) pulses. Both simulation and experimental studies were conducted to investigate the imaging properties of this new scheme with respect to Fourier schemes. Results indicate that random encoding has the potential to outperform conventional encoding in certain scenarios. However, our study also indicates that random encoding fails to satisfy theoretical sufficient conditions for stable and accurate CS reconstruction in many scenarios of interest. Therefore, there is still no general theoretical performance guarantee for CS-MRI, with or without random encoding, and CS-based methods should be developed and validated carefully in the context of specific applications.

Digital-Assisted Asynchronous Compressive Sensing Front-End

“…In a random demodulator, the mixer and integrator are required to operate continuously during the measurement generation. By (10), with the accumulated chipping waveform, a single multiplication is sufficient for each constant section. Because is a discrete sequence in the CS front-end, multiplication and integration in (10) can be efficiently implemented by a multiplier and an accumulator in digital circuitry rather than employing a dedicated mixer and integrator in the analog domain.…”

“…The CS technique integrates sampling and compression into one step, reducing the sampling directly from the analog front-end. Because of its sub-Nyquist sampling ability, the CS framework has shown potential in many applications, such as medical imaging [10], communications [11], machine learning [12], statistical signal processing [13], and geophysics [14].…”

Spread spectrum for compressed sensing techniques in magnetic resonance imaging

“…Let us acknowledge the fact that the interest of compressed sensing for MRI was already proven [6]. The introduction of a signal modulation was recently proposed and tested on real data [7], but no theoretical underpinning neither guarantees relative to the reconstruction quality was proposed. Very recently, the spread spectrum technique proposed here was extensively studied by three of the authors in the context of radio interferometry [8,9].…”

Block sparse vector recovery via weighted generalized range space property

“…Compressed Sensing (CS) and Sparse Signal Recovery emerge in many signal processing applications, including biomedical imaging [1], [5], [13], [15], [19], and radar [3], [4], [11], [14], [20]. In sparse signal recovery, we are interested in finding the best possible representation for the observation vector using a vector with the smallest number of non-zero entries.…”