Accelerated 3D phase-contrast imaging using adaptive compressed sensing with no free parameters

Introduction Compressed Sensing (CS) theory [1] allows one to use the sparsity of images in a transform domain (e.g. wavelets) effectively to enable image reconstruction with sub-Nyquist sampled data. While CS methodologies present several potential benefits for medical imaging applications (e.g. reduced scan times, higher resolution imaging, etc.), their successful implementation on clinical scanners will require robust algorithms that can automatically account for patient-to-patient and anatomical variability in the images. Typical image reconstruction algorithms employing CS theory in the literature are iterative in nature and solve the problem of minimizing a cost function consisting of an L2-norm error (or data consistency) term and one or more L1-norm terms that impose the transform domain sparsity constraints. In particular, two classes of algorithms are commonly used: (1) Non-linear conjugate gradient (NLCG) [2], and (2) iterative soft thresholding (ST) [3] approaches. The NLCG method has good convergence properties, but is sensitive to the choice of relative weights on the L1-norm penalty terms that have to be selected empirically on a case-by-case basis. NLCG algorithms may also involve computationally intensive cost function / derivative evaluations and line searches. The ST approach in the wavelet domain is leaner to implement but is also sensitive to the choice of the thresholding parameter and is slow to converge. In this paper we describe a robust and fully data driven approach to CS reconstruction in the ST framework that uses a Nesterov type [4,5] 2-step optimal gradient scheme for fast convergence properties along with adaptive wavelet denoising for imposition of the L1-sparsity constraint. For illustration we combine this CS algorithm with image domain parallel imaging (SENSE) and apply it to brain vasculature phase-contrast imaging. The reconstructed angiograms were scored blindly for image quality by an experienced neuroradiologist. Methods In describing our approach for combining the CS algorithm with parallel imaging, the data acquired for each of the echoes from a 3D phase contrast pulse sequence may be represented as f y j CSP FT j , Φ Φ = where yj is a vector of k-space measurements from the j-th coil, f is the image to be determined, ΦFT is the Fourier