Magnetic resonance imaging (MRI) is inherently a very inefficient imaging modality that requires as much polarization of the proton spins as possible [1]. For this reason, there has been a push toward higher and higher field strengths for human imaging from 3 T to 7 T and, more recently, to almost 12 T [2,3]. There are five major reasons to do so: 1) better signal-to-noise ratio (SNR), 2) better spatial resolution, 3) faster imaging, 4) novel contrast mechanisms and 5) better spectral resolution. But there are problems with imaging at high field. First, these systems are very expensive. Second, running the same sequence run at low fields leads to much higher power deposition (the power deposition increases as the square of the field). And third, imaging at high fields leads to worse susceptibility artifacts for a given echo time (TE) and requires greater gradient strengths to compensate for these field variations. As the bandwidth increases, the SNR decreases and so the expected SNR under these conditions only increases with the square root of the main field strength. Therefore, it is important practically to increase the SNR particularly for low field strengths.

One way to accomplish this is to average the data. Unfortunately, acquiring the data N times takes N times longer yet only gives a N improvement in SNR. A more commonly used approach is to filter the data. Some conventionally used filters include: Hanning, median, mean, Gaussian, bilateral or anisotropic diffusion filters. These can all improve the SNR but also lead to blurring and possible loss of small features [4]. The real question is: “How can we improve the SNR and, hence, image quality without affecting the spatial resolution in the process?” Another denoising method referred to as a non-local mean (NLM) [[5], [6], [7]] and its enhanced versions [8] can remove the Rician noise in MRI effectively and preserve the fine structures. However, the computational cost and burden of the NLM approach are higher due to its complexity of calculating the optimal window size [9]. Moreover, some other denoising techniques such as wavelet-domain filtering and statistical methods have been proposed and studied [10]. However, all these approaches have their own limitations. A review and comparison of these methods has been discussed previously [11,12]. Newer techniques are using deep-learning-based algorithms by training different models to reduce noise [[13], [14], [15], [16], [17], [18], [19]]. However, these models are typically trained using a single type of image contrast and will only work for that contrast. And, from a practical point of view, they need to be trained over a large number of cases for different acquisition methods [13,20,21]. Low rank approximations have also been used as a denoising method for MR spectroscopic image [22], dynamic myocardial T1 mapping [23] and diffusion-weighted magnitude data [24,25]. However, the performance of all these methods in the presence of abnormalities in denoising structural images still needs further investigation.

In the end, most of these algorithms lead to some degradation of the image which is recognizable as a remnant blurring relative to the original data. Our goal is to show that, with the appropriate constraints, one can obtain enhanced SNR without the loss of detail. We call this approach CROWN which stands for “Constrained Reconstruction of White Noise”. CROWN is a pixel-by-pixel algorithm that has no cross talk and hence no blurring. It uses the linear relationship between proton spin density (PSD) and T1 [[26], [27], [28]]. The linear relationship between R1 (1/T1) and β (1/PSD) has been verified in a variety of studies even at different field strengths [[26], [27], [28],[34], [35], [36], [37]]. This simple linear form is a robust and subject-independent model and avoids overfitting the data [29,30].

First, we introduce the concept behind CROWN, then evaluate it using the PSD and T1 maps generated from the strategically acquired gradient echo (STAGE) data. STAGE imaging is a rapid, multi-contrast, multi-echo, gradient echo imaging method [[31], [32], [33]]. It uses at least two flip angles to estimate PSD and T1 maps. Since CROWN runs directly on the PSD map, not on the MRI magnitude images, it is possible to apply this method for any approach generating proton spin density (PSD) and T1 maps. In this paper, we show that CROWN can be used to reduce the noise level in the STAGE PSD and R2⁎ images, and then generate higher quality synthetic images for any given imaging parameters such as flip angle, repetition time (TR), and TE. CROWN is especially powerful at reducing noise when applied to data with low SNR and may have an immediate impact in improving the data quality collected with: high parallel imaging acceleration factors (where the noise is much worse in the center of the image compared to the edge); high resolution; or from radiofrequency receive coils with a small number of channels.