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Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…
Closed-loop architecture is widely utilized in automatic control systems and attain distinguished performance. However, classical compressive sensing systems employ open-loop architecture with separated sampling and reconstruction units.…
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…
Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies: The effort of quantum tomography---the characterization of processes and states within a quantum…
We study quantum process tomography given the prior information that the map is a unitary or close to a unitary process. We show that a unitary map on a $d$-level system is completely characterized by a minimal set of $d^2{+}d$ elements…
In this paper, we consider the problem of multi-resolution compressed sensing (MR-CS) reconstruction, which has received little attention in the literature. Instead of always reconstructing the signal at the original high resolution (HR),…
We study compressed sensing (CS) signal reconstruction problems where an input signal is measured via matrix multiplication under additive white Gaussian noise. Our signals are assumed to be stationary and ergodic, but the input statistics…
Quantum Signal Processing (QSP) is a technique that can be used to implement a polynomial transformation $P(x)$ applied to the eigenvalues of a unitary $U$, essentially implementing the operation $P(U)$, provided that $P$ satisfies some…
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…
Compressive sensing (CS) is a signal processing technique that enables sub-Nyquist sampling and near lossless reconstruction of a sparse signal. The technique is particularly appealing for neural signal processing since it avoids the issues…
On noisy intermediate-scale quantum (NISQ) devices, expectation values of many observables are obtained through sampling-based approximations to trace-like quantities. A central limitation of this approach is destructive cancellation under…
Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not…
Quantum instruments describe both the classical outcome and the updated state associated with a quantum measurement. We ask whether these processes can be simulated using only a natural subset of resources, namely projective measurements on…
Can compression algorithms be employed for recovering signals from their underdetermined set of linear measurements? Addressing this question is the first step towards applying compression algorithms for compressed sensing (CS). In this…
In this paper, we investigate a Bayesian sparse reconstruction algorithm called compressive sensing via Bayesian support detection (CS-BSD). This algorithm is quite robust against measurement noise and achieves the performance of a minimum…
Compressed sensing (CS) is a concept that allows to acquire compressible signals with a small number of measurements. As such it is very attractive for hardware implementations. Therefore, correct calibration of the hardware is a central…
This letter investigates the joint recovery of a frequency-sparse signal ensemble sharing a common frequency-sparse component from the collection of their compressed measurements. Unlike conventional arts in compressed sensing, the…
Quantum image processing (QIP) means the quantum based methods to speed up image processing algorithms. Many quantum image processing schemes claim that their efficiency are theoretically higher than their corresponding classical schemes.…