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Ultrashort time-domain spectroscopy and field-resolved spectroscopy of molecular fingerprints are gold standards for detecting samples' constituents and internal dynamics. However, they are hindered by the Nyquist criterion, leading to…
In compressed sensing (CS), sparse signals can be reconstructed from significantly fewer samples than required by the Nyquist-Shannon sampling theorem. While non-sparse signals can be sparsely represented in appropriate transformation…
In a sensor network with remote sensor devices, it is important to have a method that can accurately localize a sound event with a small amount of data transmitted from the sensors. In this paper, we propose a novel method for localization…
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…
Data saving capability of "Compressed sensing (sampling)" in signal discretization is disputed and found to be far below the theoretical upper bound defined by the signal sparsity. On a simple and intuitive example, it is demonstrated that,…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
Compressed sensing provides an efficient framework for reconstructing wave signals from reduced measurements. For multi-channel buoy data, the three displacement components exhibit intrinsic correlations, as wave motion contributes…
We experimentally demonstrated a spectral imaging scheme with dual compressed sensing. With the dimensions of spectral and spatial information both compressed, the spectral image of a colored object can be obtained with only a single point…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
Sonography techniques use multiple transducer elements for tissue visualization. Signals detected at each element are sampled prior to digital beamforming. The sampling rates required to perform high resolution digital beamforming are…
Emerging sonography techniques often require increasing the number of transducer elements involved in the imaging process. Consequently, larger amounts of data must be acquired and processed. The significant growth in the amounts of data…
This paper proposes a compressed sensing (CS) framework for the acquisition and reconstruction of frequency-sparse signals with chaotic dynamical systems. The sparse signal is acting as an excitation term of a discrete-time chaotic system…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or…
Recent advances in signal processing have focused on the use of sparse representations in various applications. A new field of interest based on sparsity has recently emerged: compressed sensing. This theory is a new sampling framework that…
Snapshot compressed sensing (CS) refers to compressive imaging systems in which multiple frames are mapped into a single measurement frame. Each pixel in the acquired frame is a noisy linear mapping of the corresponding pixels in the frames…
This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
The fragility of quantum systems makes them ideally suited for sensing applications at the nanoscale. However, interpreting the output signal of a qubit-based sensor is generally complicated by background clutter due to out-of-band spectral…
A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…