Measure Digital, Reconstruct Analog16 Apr 2019
Inner-Loop-Free ADMM for Cryo-EM15 Jan 2019
Fast PET reconstruction: the home stretch11 Dec 2018
Self-Supervised Deep Active Accelerated MRI27 Nov 2018
Minimum Support Multi-Splines20 Nov 2018
Looking beyond Pixels: Theory, Algorithms and Applications of Continuous Sparse Recovery07 Aug 2018
Sparse recovery is a powerful tool that plays a central role in many applications. Conventional approaches usually resort to discretization, where the sparse signals are estimated on a pre-defined grid. However, the sparse signals do not line up conveniently on any grid in reality. We propose a continuous-domain sparse recovery technique by generalizing the finite rate of innovation (FRI) sampling framework to cases with non-uniform measurements. We achieve this by identifying a set of unknown uniform sinusoidal samples (which are related to the sparse signal parameters to be estimated) and the linear transformation that links the uniform samples of sinusoids to the measurements. It is shown that the continuous-domain sparsity constraint can be equivalently enforced with a discrete convolution equation of these sinusoidal samples. Then, the sparse signal is reconstructed by minimizing the fitting error between the given and the re-synthesized measurements (based on the estimated sparse signal parameters) subject to the sparsity constraint. Further, we develop a multi-dimensional sampling framework for Diracs in two or higher dimensions with linear sample complexity. This is a significant improvement over previous methods, which have a complexity that increases exponentially with space dimension. An efficient algorithm has been proposed to find a valid solution to the continuous-domain sparse recovery problem such that the reconstruction (i) satisfies the sparsity constraint; and (ii) fits the given measurements (up to the noise level). We validate the flexibility and robustness of the FRI-based continuous-domain sparse recovery in both simulations and experiments with real data in radioastronomy, acoustics and microscopy.