In this work, we extend the sparse iterative covariance-based estimator (SPICE), by generalizing the formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. For a given norm, the resulting extended SPICE method enjoys the same benefits as the regular SPICE method, including being hyper-parameter free, although the choice of norms are shown to govern the sparsity in the resulting solution. Furthermore, we show that solving the extended SPICE method is equivalent to solving a penalized regression problem, which provides an alternative interpretation of the proposed method and a deeper insight on the differences in sparsity between the extended and the original SPICE formulation. We examine the performance of the method for different choices of norms, and compare the results to the original SPICE method, showing the benefits of using the extended formulation. We also provide two ways of solving the extended SPICE method; one gridbased method, for which an efficient implementation is given, and a gridless method for the sinusoidal case, which results in a semi-definite programming problem.
Identification of prostate gold fiducial markers in magnetic resonance imaging (MRI) images is challenging when CT images are not available, due to misclassifications from intra-prostatic calcifications. It is also a time consuming task and automated identification methods have been suggested as an improvement for both objectives. Multi-echo gradient echo (MEGRE) images have been utilized for manual fiducial identification with 100% detection accuracy. The aim is therefore to develop an automatic deep learning based method for fiducial identification in MRI images intended for MRI-only prostate radiotherapy. MEGRE images from 326 prostate cancer patients with fiducials were acquired on a 3T MRI, post-processed with N4 bias correction, and the fiducial center of mass (CoM) was identified. A 9 mm radius sphere was created around the CoM as ground truth. A deep learning HighRes3DNet model for semantic segmentation was trained using image augmentation. The model was applied to 39 MRI-only patients and 3D probability maps for fiducial location and segmentation were produced and spatially smoothed. In each of the three largest probability peaks, a 9 mm radius sphere was defined. Detection sensitivity and geometric accuracy was assessed. To raise awareness of potential false findings a ‘BeAware’ score was developed, calculated from the total number and quality of the probability peaks. All datasets, annotations and source code used were made publicly available. The detection sensitivity for all fiducials were 97.4%. Thirty-six out of thirty-nine patients had all fiducial markers correctly identified. All three failed patients generated a user notification using the BeAware score. The mean absolute difference between the detected fiducial and ground truth CoM was 0.7 ± 0.9 [0 3.1] mm. A deep learning method for automatic fiducial identification in MRI images was developed and evaluated with state-of-the-art results. The BeAware score has the potential to notify the user regarding patients where the proposed method is uncertain.
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