Synopsis We investigate the feasibility of using 2-D self-navigation for respiratory gating for free-breathing whole-heart 3-D CINE imaging, where respirationinduced cardiac motion may be more easily detected than in commonly used 1-D self-navigation methods. We compare self-navigation images, derived gating signals and resulting 3-D CINE images of the 1-D and 2-D methods and nd that respirator...

In this note, we summarize the results we recently proved in [14] on the theoretical performance guarantees of the decoders ∆p. These decoders rely on ` minimization with p ∈ (0, 1) to recover estimates of sparse and compressible signals from incomplete and inaccurate measurements. Our guarantees generalize the results of [2] and [16] about decoding by `p minimization with p = 1, to the setting...

The goal of sparse recovery is to recover the (approximately) best k-sparse approximation x̂ of an n-dimensional vector x from linear measurements Ax of x. We consider a variant of the problem which takes into account partial knowledge about the signal. In particular, we focus on the scenario where, after the measurements are taken, we are given a set S of size s that is supposed to contain most...

Over the recent years, a new *linear* method for compressing high-dimensional data (e.g., images) has been discovered. For any high-dimensional vector x, its *sketch* is equal to Ax, where A is an m x n matrix (possibly chosen at random). Although typically the sketch length m is much smaller than the number of dimensions n, the sketch contains enough information to recover an *approximation* t...

We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via l1-l1 and l1-l2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruc...

Traditional video capture is limited by the trade-off between spatial and temporal resolution. When capturing videos of high temporal resolution, the spatial resolutions decreases due to bandwidth limitations in the capture system. Achieving both high spatial and temporal resolution is only possible with highly specialized and very expensive hardware; although the bandwidth is higher, the same ...

We present two recursive techniques to construct compressed sensing schemes that can be “decoded" in sub-linear time. The first technique is based on the well studied code composition method called code concatenation where the “outer" code has strong list recoverability properties. This technique uses only one level of recursion and critically uses the power of list recovery. The second recursi...

Compressed sensing is a relatively new signal processing technique whereby the limits proposed by the Shannon-Nyquist theorem can be exceeded under certain conditions imposed upon the signal. Such conditions occur in many real-world scenarios, and compressed sensing has emerging applications in medical imaging, big data, and statistics. Finding practical matrix constructions and computationally...

A general echo model is derived for the synthetic aperture radar (SAR) imaging with high resolution based on the scalar form of Maxwell’s equations. After analyzing the relationship between the general echo model in frequency domain and the existing model in time domain, a compressive sensing (CS) matrix is constructed from random partial Fourier matrices for processing the range CS SAR imaging...

Compressive sensing (CS) is an emerging methodology in computational signal processing that has recently attracted intensive research activities. At present, the basic CS theory includes recoverability and stability: the former quantifies the central fact that a sparse signal of length n can be exactly recovered from far fewer than n measurements via 1-minimization or other recovery techniques,...