We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The reconstruction method relies on the recently demonstrated sparsity-based sub-wavelength imaging. However, for partially-spatially-incoherent light, the relation bet...

We extend ideas from compressive sensing to a structured sparsity model related to fusion frames. We present theoretical results concerning the recovery of sparse signals in a fusion frame from undersampled measurements. We provide both nonuniform and uniform recovery guarantees. The novelty of our work is to exploit an incoherence property of the fusion frame which allows us to reduce the numb...

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in [1] to recover 1-dimensional spectrally sparse signal. However, in spite of existing research efforts [2], ...

The problem of imaging periodic structure (source or scatterer) is formulated in the framework of compressed sensing with special attention on subwavelength resolution. It is shown that in this formulation the subwavelength resolution in the presence of noise can not be achieved by compressed sensing techniques alone. Additional techniques such as near-field measurement or illumination are requ...

The analysis of ISAR image recovery from a reduced set of data presented in [1] is extended in this correspondence to an important topic of signal nonsparsity (approximative sparsity). In real cases the ISAR images are noisy and only approximately sparse. Formula for the mean square error in the nonsparse ISAR, reconstructed under the sparsity assumption, is derived. The results are tested on e...

The potential of compressive sensing (CS) has spurred great interest in the research community and is a fast growing area of research. However, research translating CS theory into practical hardware and demonstrating clear and significant benefits with this hardware over current, conventional imaging techniques has been limited. This article helps researchers to find those niche applications wh...

When 3-D models of environments need to be transmitted or stored, they should be compressed efficiently to increase the capacity of the communication channel or the storage medium. We propose a novel compression technique based on compressive sensing, applied to sparse representations of 3-D range measurements. We develop a novel algorithm to generate sparse innovations between consecutive rang...

In compressed sensing, one wishes to acquire an approximately sparse high-dimensional signal x ∈ R via m n noisy linear measurements, then later approximately recover x given only those measurement outcomes. Various guarantees have been studied in terms of the notion of approximation in recovery, and some isolated folklore results are known stating that some forms of recovery are stronger than ...

In this paper, we address the theoretical limitations in reconstructing sparse signals (in a known complete basis) using compressed sensing framework. We also divide the CS to non-blind and blind cases. Then, we compute the Bayesian Cramer-Rao bound for estimating the sparse coefficients while the measurement matrix elements are independent zero mean random variables. Simulation results show a ...

images of the two simultaneously excited slices. Displayed are (a) the conventional reconstruction of the CAIPIRINHA acquisition using GRAPPA and (b) the reconstruction of the incoherently undersampled CAIPIRINHA acquisition using the proposed combination of Compressed Sensing and GRAPPA. (c) Difference between a) and b) magnified by a factor of 10. Accelerated Simultaneous Multi-slice Cardiac ...