Is compressive sensing overrated? Or can it live up to our expectations? What will come after compressive sensing and sparsity? And what has Galileo Galilei got to do with it? Compressive sensing has taken the signal processing community by storm. A large corpus of research devoted to the theory and numerics of compressive sensing has been published in the last few years. Moreover, compressive ...

Compressive sensing provides a new framework for simultaneous sampling and compression of signals. According to compressive sensing theory one can recover compressible signals and images from far fewer samples or measurements that traditional methods use. Applying compressive sensing theory for holography comes natural since three-dimensional (3D) data is typically very redundant, thus it is al...

In a series of recent work [5, 4], the theory of compressive sensing has been examined from an information theory perspective. Novel results regarding noisy compressive sensing have been found while viewing the compressive sensing problem as a communication channel. This perspective led to a new approach of solving the compressive sensing problem through a Bayesian approach. Belief propagation,...

A method of spectral sensing based on compressive sensing is shown to have the potential to achieve high resolution in a compact device size. The random bases used in compressive sensing are created by the optical response of a set of different nanophotonic structures, such as photonic crystal slabs. The complex interferences in these nanostructures offer diverse spectral features suitable for ...

Compressive sensing (CS) is a framework in which one attempts to measure a signal in a compressive mode, implying that fewer total measurements are required vis-à-vis direct sampling methods. Compressive sensing exploits the fact that the signal of interest is compressible in some basis, and the CS measurements correspond to projections (typically random projections) performed on the basisfunct...

Compressive sensing is a sampling method which provides a new approach to efficient signal compression and recovery by exploiting the fact that a sparse signal can be suitably reconstructed from very few measurements. One of the most concerns in compressive sensing is the construction of the sensing matrices. While random sensing matrices have been widely studied, only a few deterministic sensi...

In recent years compressive sensing has been successfully introduced in digital holography. Depending on the ability to sparsely represent an object, the compressive sensing paradigm provides an accurate object reconstruction framework, from a relatively small number of encoded signal samples. Digital holography has been proven to be an efficient and physically realizable sensing modality that ...

Concepts of directional remote sensing are put forward based on two-dimensional compressive sensing. Very little measured data are required to acquire and reconstruct change areas in directional remote sensing. The measured data in one-dimensional compressive sensing not only keep the energy of a sparse signal, but also inherit the sparse signal’s direction information. However, direction infor...

Michael B. Wakin is the Ben L. Fryrear Associate Professor in the Department of Electrical Engineering and Computer Science at the Colorado School of Mines (CSM). Dr. Wakin received a B.S. in electrical engineering and a B.A. in mathematics in 2000 (summa cum laude), an M.S. in electrical engineering in 2002, and a Ph.D. in electrical engineering in 2007, all from Rice University. He was an NSF...