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The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…
Cameras for imaging in short and mid-wave infrared spectra are significantly more expensive than their counterparts in visible imaging. As a result, high-resolution imaging in those spectrum remains beyond the reach of most consumers. Over…
We present the first fully two-dimensional attenuation imaging technique developed for pulse-echo ultrasound systems. Unlike state-of-the-art techniques, which use line-by-line acquisitions, our method uses steered emissions to constrain…
In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…
In compressed sensing (CS) framework, a signal is sampled below Nyquist rate, and the acquired compressed samples are generally random in nature. However, for efficient estimation of the actual signal, the sensing matrix must preserve the…
The volume of remote sensing data is experiencing rapid growth, primarily due to the plethora of space and air platforms equipped with an array of sensors. Due to limited hardware and battery constraints the data is transmitted back to…
Compressed sensing (CS) is a powerful tool for reducing the amount of data to be collected while maintaining high spatial resolution. Such techniques work well in practice and at the same time are supported by solid theory. Standard CS…
Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. The current methods for computational time reversal imaging are based on the null subspace projection operator,…
Recent ultrasound imaging modalities based on ultrasound computed tomography indicate a huge potential to detect pathologies is tissue due to altered biomechanical properties. Especially the imaging of speed-of-sound (SoS) distribution in…
Inverse obstacle scattering is the recovery of an obstacle boundary from the scattering data produced by incident waves. This shape recovery can be done by iteratively solving a PDE-constrained optimization problem for the obstacle…
Ultra low radiation dose in X-ray Computed Tomography (CT) is an important clinical objective in order to minimize the risk of carcinogenesis. Compressed Sensing (CS) enables significant reductions in radiation dose to be achieved by…
This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
Compressed sensing (CS) is a valuable technique for reconstructing measurements in numerous domains. CS has not yet gained widespread adoption in scanning tunneling microscopy (STM), despite potentially offering the advantages of lower…
Quadrature sampling has been widely applied in coherent radar systems to extract in-phase and quadrature (I and Q) components in the received radar signal. However, the sampling is inefficient because the received signal contains only a…
Compressive sensing (CS) works to acquire measurements at sub-Nyquist rate and recover the scene images. Existing CS methods always recover the scene images in pixel level. This causes the smoothness of recovered images and lack of…
Random pulse sequences are a powerful method for qubit noise spectroscopy, enabling efficient reconstruction of sparse noise spectra. Here, we advance this method in two complementary directions. First, we extend the method using a…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
Imaging by aperture synthesis from interferometric data is a well-known, but is a strong ill-posed inverse problem. Strong and faint radio sources can be imaged unambiguously using time and frequency integration to gather more Fourier…