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We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP)…
In MR fingerprinting (MRF) reconstruction, measured data is pattern-matched to simulated signals to extract quantitative tissue parameters. A critical drawback to this approach is the exponentially increasing compute time for mapping of…
The Nyquist-Shannon theorem states that the information accessible by discrete Fourier protocols saturates when the sampling rate reaches twice the bandwidth of the detected continuous time signal. This maximum rate (the NS-limit) plays a…
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…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
We consider the problem of signal estimation in a generalized linear model (GLM). GLMs include many canonical problems in statistical estimation, such as linear regression, phase retrieval, and 1-bit compressed sensing. Recent work has…
Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse…
Iterative thresholding algorithms are well-suited for high-dimensional problems in sparse recovery and compressive sensing. The performance of this class of algorithms depends heavily on the tuning of certain threshold parameters. In…
Purpose: To propose and evaluate an accelerated $T_{1\rho}$ quantification method that combines $T_{1\rho}$-weighted fast spin echo (FSE) images and proton density (PD)-weighted anatomical FSE images, leveraging deep learning models for…
Parallel imaging has been an essential technique to accelerate MR imaging. Nevertheless, the acceleration rate is still limited due to the ill-condition and challenges associated with the undersampled reconstruction. In this paper, we…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Magnetic Resonance Imaging (MRI) is a powerful, non-invasive diagnostic tool; however, its clinical applicability is constrained by prolonged acquisition times. Whilst present deep learning-based approaches have demonstrated potential in…
Recently, Approximate Message Passing (AMP) has been integrated with stochastic localization (diffusion model) by providing a computationally efficient estimator of the posterior mean. Existing (rigorous) analysis typically proves the…
Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal…
Dynamic MRI reconstruction from undersampled measurements is a challenging inverse problem that requires preserving both spatial reconstruction quality and temporal consistency across the frames of the cine series. While recent…
High-dimensional signal recovery of standard linear regression is a key challenge in many engineering fields, such as, communications, compressed sensing, and image processing. The approximate message passing (AMP) algorithm proposed by…
Objective: To propose and validate an unsupervised MRI reconstruction method that does not require fully sampled k-space data. Materials and Methods: The proposed method, deep image prior with structured sparsity (DISCUS), extends the deep…
We present an analytical inversion technique which can be used to recover ionization probabilities from spatially averaged data in an N-dimensional detection scheme. The solution is given as a power series in intensity. For this reason, we…
To reduce scanning time and/or improve spatial/temporal resolution in some MRI applications, parallel MRI (pMRI) acquisition techniques with multiple coils acquisition have emerged since the early 1990s as powerful 3D imaging methods that…