Multichannel Compressive Sensing MRI Using Noiselet Encoding

Abstract: The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP) of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS). In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the incoherence between the randomly under-sampled Fourier matrix and the wavelet matrix is not optimal, which can deteriorate the performance of CS-MRI. Using the mathematical result that noiselets are maximally incoherent with wavelets, this paper introduces the noiselet unitary bases as the measurement matrix to improve the incoherence and RIP in CS-MRI, and presents a method to design the pulse sequence for the noiselet encoding. This novel encoding scheme is combined with the multichannel compressive sensing (MCS) framework to take the advantage of multichannel data acquisition used in MRI scanners. An empirical RIP analysis is presented to compare the multichannel noiselet and multichannel Fourier measurement matrices in MCS. Simulations are presented in the MCS framework to compare the performance of noiselet encoding reconstructions and Fourier encoding reconstructions at different acceleration factors. The comparisons indicate that multichannel noiselet measurement matrix has better RIP than that of its Fourier counterpart, and that noiselet encoded MCS-MRI outperforms Fourier encoded MCS-MRI in preserving image resolution and can achieve higher acceleration factors. To demonstrate the feasibility of the proposed noiselet encoding scheme, two pulse sequences with tailored spatially selective RF excitation pulses was designed and implemented on a 3T scanner to acquire the data in the noiselet domain from a phantom and a human brain.

Multichannel Compressive Sensing MRI Using Noiselet Encoding

The paper presents a novel method for improving the performance of Compressive Sensing Magnetic Resonance Imaging (CS-MRI) through the use of noiselet encoding and multichannel imaging. The research identifies key components of compressive sensing, such as incoherence between measurement and sparsifying transform matrices, and explores how adjustments using noiselets can lead to enhanced RIP with multichannel data acquisition systems in MRI.

The authors address the problem of suboptimal incoherence between the randomly under-sampled Fourier matrix usually employed in CS-MRI and the wavelet matrix used for sparsifying transformations. Fourier encoding in the MRI process results in inefficient spreading of signal energy, necessitating more stringent undersampling requirements and ultimately hindering acceleration factors. By introducing noiselet bases, which exhibit maximal incoherence with wavelet transforms, the research proposes an encoding system that significantly advances the RIP properties of measurement matrices.

The comparative results are critical; the experimental results show that noiselet encoding achieves higher acceleration factors while preserving image resolution more effectively than traditional Fourier encoding methods. Two tailored pulse sequences were tested on a 3T scanner, acquiring both phantom and human brain data, demonstrating the feasibility of the approach. This data suggests that noiselet encoding in combination with multichannel compressive sensing (MCS-MRI) is particularly useful for applications requiring high-resolution imaging.

Further analysis shows that the multichannel noiselet measurement matrices indeed have stronger RIP characteristics compared to their Fourier counterparts, validating the approach as a method that not only retains but enhances MRI image quality, especially under higher acceleration factors. These strong RIP properties and maximal incoherence ensure that image reconstruction remains faithful to the original signal, even when undersampled.

The authors discuss practical limitations of current non-Fourier implementations, including sensitivity to field inhomogeneities and signal-to-noise ratio complications. They offer insights into potential improvements, such as applying the noiselet encoding to 3D gradient echo sequences instead of spin echoes, leveraging parallel-transmit technologies, and mitigating the effects of inhomogeneity through advanced pulse design.

The prospective developments in pulse design and parallel-transmit techniques could further enhance the efficiency and applicability of noiselet encoding in clinical settings. These advancements may potentially overcome existing hardware limitations and pave the way for more consistent applications of noiselet encoding across diverse MRI systems.

In conclusion, the paper conclusively demonstrates that using noiselet encoding within an MCS-MRI framework shows significant promise in accelerating MRI scanning processes and improving image reconstruction quality. The findings suggest a potential shift in how compressive sensing in MRI is approached, advocating for encoding strategies that better exploit signal sparsity characteristics and channel diversity inherent in multichannel imaging systems.