As a powerful and non-invasive medical imaging tool, functional Magnetic Resonance Imaging (fMRI) has played a dominant role in brain imaging studies since 1990 [1]. Neuronal activity cannot be directly detected but correlates with the Blood Oxygen Level Dependence (BOLD) contrast signal which is used as a proxy. By detecting task-related changes in the BOLD signal inside our brain, the magnetic resonance (MR) scanner can map our brain with a unique radio frequency (RF) pulse sequence [1], [2]. In structural and functional MRI studies, the time to measure a volume image is dependent upon how rapidly the amount of data necessary to reconstruct an image can be measured. In order to accelerate the number of images measured per unit time, a topic of study has been to measure less data but still be able to reconstruct a high-quality image. To reconstruct images using less data, multiple receiver coils are used where each coil measures sensitivity-weighted images [3]. Initially, accelerated imaging was aimed at In-Plane Acceleration (IPA) where spatial frequency data are partially skipped, and each coil measured fewer lines of the spatial frequency array. Parallel imaging techniques, such as Sensitivity Encoding (SENSE) and Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) [4], [5], can be incorporated with the IPA techniques. Bayesian techniques have been applied to improve the resolution of the reconstructed images by incorporating the anatomical information from prior distributions into the k-space [6], [7]. Other in-plane imaging acceleration techniques like partial Fourier imaging technique [8], [9] can acquire half of the lines in the k-space. However, considering some fixed time blocks in the data-acquiring process, for instance, imaging encoding and the proper time for T2∗ contrast in one excitation, the scan time will not decrease significantly in IPA techniques. More recently, Simultaneous Multi-Slice (SMS) techniques (Fig. 1) were developed and discussed [10], [11], [12]. The SMS technique is extensively used in fMRI studies, and it allows for acquiring fMRI data with high resolution by using a multiband (MB) radiofrequency (RF) within a reduced repetition time (TR). Compared with conventional parallel imaging techniques, in SMS techniques, multiple slices are acquired concurrently and aliased together in one excitation, and hence, the image-acquiring time will decrease with a factor of the total number of aliased slices. Thus, a Through-Plane Acceleration (TPA) is achieved by SMS techniques and allows for a more efficient approach to acquiring images.

Since multiple slices are acquired at the same time for one excitation of the TPA technique, a short distance between aliased slices will lead to a high similarity of voxel and coil sensitivity information. When applying the standard SENSE method, this may cause a singular matrix problem and strong inter-slice signal leakage will appear on the reconstructed images. To decrease the influence of the geometry properties of the coil sensitivity maps, techniques like “controlled aliasing in parallel imaging results in higher acceleration” (CAIPIRINHA), “blipped-CAIPIRINHA” (Blipped-CAIPI), and Hadamard phase-encoding provide other possible ways to minimize the influence of the geometric factor (g-factor) and increase the conditioning of the slices aliasing matrix [13], [14]. By modulating the phase for each line in k-space and imparting each line with a specific angle, the field-of-view (FOV) is shifted in the phase-encoding direction (PE, vertically in this paper). Applying a unique phase modulation amount to each slice in the aliased image-acquiring process increases the physical distance between the aliased voxels. Therefore, the difference of coil sensitivity for each slice will increase and the influence of the g-factor for each excitation is minimized. Moreover, to further increase the physical distance between two aliased voxels and expose more information beneath the coil sensitivities, the FOV cannot only be moved along the vertical PE direction but also the horizontal readout direction (RO, horizontally in this paper). The study “multislice CAPIPRINHA using view angle tilting technique” (CAIPIVAT) [15], [16] proposes a method combining the CAIPIRINHA technique and View Angle Tilting (VAT) [17] technique together by applying a unique compensation gradient of VAT. The inter-slice signal leakage can be reduced using the slice-GRAPPA and split slice-GRAPPA approaches by applying GRAPPA kernels to the k-space of the aliased slices [14], [18]. Other techniques to solve the singular matrix problem of the design matrix, like the “simultaneous multi-slice acquisition” (SIMA) [10] method discussed a powerful tool, the Hadamard phased-encoding technique in the reconstruction process. By incorporating a specific coefficient from the Hadamard matrix for each aliasing slice, different combinations for each voxel is achieved. For example, the summation of two desired voxels will not only be acquired but also the difference between two voxels is collected. Moreover, the Hadamard phase-encoding technique has been proved to be a significant method to minimize the residual correlation between the unaliased images and improve the temporal signal-to-noise ratio (tSNR) [19], [20]. In the “Separation of parallel encoded complex-valued slices (SPECS) from a single complex-valued aliased coil image” and “multi-coil separation of parallel encoded complex-valued slices” (mSPECS) studies, the Hadamard phase encoding technique is also the essential idea [21], [22].

In the Bayesian Controlled Aliasing in Parallel Imaging with View Angle Tilting approach for multi-coil Separation of Parallel Encoded Complex-valued Slices (mSPECS-CAIPIVAT) model, we incorporate slice-wise image shift techniques and the Hadamard phase-encoding technique together in which different voxel combinations is acquired for each excitation. It provides a solution to significantly reduce the scan time with a high acceleration factor, meanwhile providing high-resolution and high-quality reconstruction images. The mSPECS-CAIPIVAT model would not only advance the methodology of Bayesian fMRI image reconstruction but also benefit clinical and practical applications. In the mSPECS-CAIPIVAT model, since multiple slices are acquired concurrently, the total image acquisition time is reduced by a factor corresponding to the number of aliased slices per excitation. This reduction in acquisition time greatly improves the efficiency of fast-imaging protocols and alleviates discomfort for patients, such as those with claustrophobia, during fMRI experiments. Moreover, compared with traditional multiband fMRI acquisition methods, the mSPECS-CAIPIVAT model provides a higher activation detection rate in task-related brain areas in less time.