In this work, we incorporated the Feature Refinement (FR) scheme into the Self-supporting Tailored k-space Estimation for Parallel imaging reconstruction (STEP) image reconstruction framework to enhance its capability for structural representation in image domain, and developed a novel Weber Local Descriptor (WLD) method to improve the extraction of local image boundaries. With the preliminary experiments, it has been demonstrated that the improved STEP with WLD FR scheme can provide more accurate estimation of image details in comparison to original STEP and existing classic method.
Incorporation of feature refinement
The FR module is introduced after the low rank and sparse approximation of local subspace basis and weighting matrix3. Since this approximation might suppress both noise-like artifacts and image details, it has the potential to capture some useful image features from the residuals and this feature refined image will be exploited as a Tikhonov regularization for the estimation of unacquired k-space data (Figure 1). The local image descriptor will be estimated on the Sum Of Squares (SOS) of the multi-channel images and weighted by the magnitude of sensitivity maps (which can be estimated by either ESPIRiT5 or scaling the magnitude image of each channel by the SOS image) to obtain its multi-channel counterpart, which can reduce the adverse impact of spatially varying signal-to-noise variations of surface coil for multi-channel image feature extraction.
Optimization of local image descriptor
Inspired by the Weber’s law6, a Weber Local Descriptor (WLD) is introduced by establishing a nonlinear transform of the ratio between image gradient magnitude and intensity. The gradient magnitude is the SOS combination of multi-directional edge detection results (e.g. image convolution with Sobel operator) and dividing it by the image intensity can measure whether the local intensity variations are noticeable in perception. In addition, the nonlinear transform (e.g. sigmoid function) of this ratio (Figure 2a) can further highlight the location of edge boundaries while reduce the interference from slow variation of image contrast in comparison to the previously proposed Structural SIMilarity based Descriptor (SSIMD) (4) (Figure 2b). Since the image sharpness depends more on the edge preservation, it’s expected that the proposed WLD can more effectively enhance the image feature extraction.
Experiment setup
Two 8-channel Cartesian T1 weighted brain datasets with/without aliasing due to small field of view were obtained from the ESPIRiT toolbox on author’s webpage7, to evaluate the performance of improved STEP with FR scheme in comparison to SPIRiT and the original STEP method. Two typically used two dimensional undersampling patterns with central autocalibration signals (ACSs) were investigated on each dataset: variable density random undersampling (the size of ACSs: 26x26, acceleration factor (AF): x5) and uniform undersampling (the size of ACSs: 35x35, AF: x4). For a better assessment of FR effect, the subspace rank value and the basis selection threshold were fixed the same for STEP with/without FR scheme. The normalized Root Mean Square Error (nRMSE) and mean SSIM index (mSSIM)8 were exploited as two criterions for quantitative image quality measurement.
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