Compressed sensing (CS) is a novel method to measure and reconstruct N-dimensional compressible signals from M << N linear-combination (e.g. Fourier-component) samples [1,2]. CS has been applied to brain MRI to achieve acceleration factors R = N/M of 2–3 with only modest degradation in image quality [3]. A further reduction in the scan time can be achieved by multi-coil parallel MRI (pMRI) [4]....

Most of compressed sensing (CS) theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications, such as signal detection, motion detection and radar. Moreover, in these applications it is often not necessary to know the support of the signal exactly, but ...

Introduction: Flexible radial imaging allows multiple image sets, each having a different spatiotemporal balance, to be retrospectively reconstructed from the same dataset [1,2]. One of the applications that may benefit from this flexibility is dynamic contrast-enhanced breast imaging, in which the optimal spatiotemporal balance for image diagnosis is unknown. Images from radial undersampling h...

The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We are motivated to study the optimal distribution of finite sampling points. Formulation under the framework of optimal reconstruction yields a minimization pro...

We propose a Conditional Density Filtering (C-DF) algorithm for efficient online Bayesian inference. C-DF adapts Gibbs sampling to the online setting, sampling from approximations to conditional posterior distributions obtained by tracking of surrogate conditional sufficient statistics as new data arrive. This tracking eliminates the need to store or process the entire data set simultaneously. ...

Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover,...

We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere, such as the canonical Driscoll & Healy sampling theorem. A reduction in the number ...

Compressive sampling is an emerging technique that promises to effectively recover a sparse signal from far fewer measurements than its dimension. The compressive sampling theory assures almost an exact recovery of a sparse signal if the signal is sensed randomly where the number of the measurements taken is proportional to the sparsity level and a log factor of the signal dimension. Encouraged...

Compressive sampling is a technique of recovering sparse N -dimensional signals from low-dimensional projections, i.e., their linear images in R,m ≪ N. In formal terms the problem can be stated as follows. Let Φ : R → R ,m ≪ N be a linear operator used to create a “sketch” of a signal represented by a real vector x ∈ R . In other words, we observe a compressed version of the signal, i.e., a vec...

In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using dictionary learning. We then perform an SVD on the dictionary and use the first few left singular vectors as the rows of the measurement matrix to obtain th...