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Register a new userLearning Sampling and Model-Based Signal Recovery for Compressed Sensing MRI
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Compressed sensing (CS) MRI relies on adequate undersampling of the k-space to accelerate the acquisition without compromising image quality. Consequently, the design of optimal sampling patterns for these k-space coefficients has received significant attention, with many CS MRI methods exploiting variable-density probability distributions. Realizing that an optimal sampling pattern may depend on the downstream task (e.g. image reconstruction, segmentation, or classification), we here propose joint learning of both task-adaptive k-space sampling and a subsequent model-based proximal-gradient recovery network. The former is enabled through a probabilistic generative model that leverages the Gumbel-softmax relaxation to sample across trainable beliefs while maintaining differentiability. The proposed combination of a highly flexible sampling model and a model-based (sampling-adaptive) image reconstruction network facilitates exploration and efficient training, yielding improved MR image quality compared to other sampling baselines.
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Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted considerable attention in recent years. Compressed sensing emerged as a popular framework for sparse signal reconstruction from a small set of compressed measurements. However, typical compressed sensing designs measure a (non)linearly weighted combination of all input signal elements, which poses practical challenges. These designs are also not necessarily task-optimal. In addition, real-time recovery is hampered by the iterative and time-consuming nature of sparse recovery algorithms. Recently, deep learning methods have shown promise for fast recovery from compressed measurements, but the design of adequate and practical sensing strategies remains a challenge. Here, we propose a deep learning solution termed Deep Probabilistic Sub-sampling (DPS), that learns a task-driven sub-sampling pattern, while jointly training a subsequent task model. Once learned, the task-based sub-sampling patterns are fixed and straightforwardly implementable, e.g. by non-uniform analog-to-digital conversion, sparse array design, or slow-time ultrasound pulsing schemes. The effectiveness of our framework is demonstrated in-silico for sparse signal recovery from partial Fourier measurements, and in-vivo for both anatomical image and tissue-motion (Doppler) reconstruction from sub-sampled medical ultrasound imaging data.
Approximate message passing (AMP) is an efficient iterative signal recovery algorithm for compressed sensing (CS). For sensing matrices with independent and identically distributed (i.i.d.) Gaussian entries, the behavior of AMP can be asymptotically described by a scaler recursion called state evolution. Orthogonal AMP (OAMP) is a variant of AMP that imposes a divergence-free constraint on the denoiser. In this paper, we extend OAMP to incorporate generic denoisers, hence the name D-OAMP. Our numerical results show that state evolution predicts the performance of D-OAMP well for generic denoisers when i.i.d. Gaussian or partial orthogonal sensing matrices are involved. We compare the performances of denosing-AMP (D-AMP) and D-OAMP for recovering natural images from CS measurements. Simulation results show that D-OAMP outperforms D-AMP in both convergence speed and recovery accuracy for partial orthogonal sensing matrices.
Magnetic resonance image (MRI) reconstruction is a severely ill-posed linear inverse task demanding time and resource intensive computations that can substantially trade off {it accuracy} for {it speed} in real-time imaging. In addition, state-of-the-art compressed sensing (CS) analytics are not cognizant of the image {it diagnostic quality}. To cope with these challenges we put forth a novel CS framework that permeates benefits from generative adversarial networks (GAN) to train a (low-dimensional) manifold of diagnostic-quality MR images from historical patients. Leveraging a mixture of least-squares (LS) GANs and pixel-wise $ell_1$ cost, a deep residual network with skip connections is trained as the generator that learns to remove the {it aliasing} artifacts by projecting onto the manifold. LSGAN learns the texture details, while $ell_1$ controls the high-frequency noise. A multilayer convolutional neural network is then jointly trained based on diagnostic quality images to discriminate the projection quality. The test phase performs feed-forward propagation over the generator network that demands a very low computational overhead. Extensive evaluations are performed on a large contrast-enhanced MR dataset of pediatric patients. In particular, images rated based on expert radiologists corroborate that GANCS retrieves high contrast images with detailed texture relative to conventional CS, and pixel-wise schemes. In addition, it offers reconstruction under a few milliseconds, two orders of magnitude faster than state-of-the-art CS-MRI schemes.
Reconstructing under-sampled k-space measurements in Compressed Sensing MRI (CS-MRI) is classically solved with regularized least-squares. Recently, deep learning has been used to amortize this optimization by training reconstruction networks on a dataset of under-sampled measurements. Here, a crucial design choice is the regularization function(s) and corresponding weight(s). In this paper, we explore a novel strategy of using a hypernetwork to generate the parameters of a separate reconstruction network as a function of the regularization weight(s), resulting in a regularization-agnostic reconstruction model. At test time, for a given under-sampled image, our model can rapidly compute reconstructions with different amounts of regularization. We analyze the variability of these reconstructions, especially in situations when the overall quality is similar. Finally, we propose and empirically demonstrate an efficient and data-driven way of maximizing reconstruction performance given limited hypernetwork capacity. Our code is publicly available at https://github.com/alanqrwang/RegAgnosticCSMRI.
Compressed Sensing MRI (CS-MRI) has shown promise in reconstructing under-sampled MR images, offering the potential to reduce scan times. Classical techniques minimize a regularized least-squares cost function using an expensive iterative optimization procedure. Recently, deep learning models have been developed that model the iterative nature of classical techniques by unrolling iterations in a neural network. While exhibiting superior performance, these methods require large quantities of ground-truth images and have shown to be non-robust to unseen data. In this paper, we explore a novel strategy to train an unrolled reconstruction network in an unsupervised fashion by adopting a loss function widely-used in classical optimization schemes. We demonstrate that this strategy achieves lower loss and is computationally cheap compared to classical optimization solvers while also exhibiting superior robustness compared to supervised models. Code is available at https://github.com/alanqrwang/HQSNet.
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