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Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage…
Scene-dependent adaptive compressive sensing (CS) has been a long pursuing goal which has huge potential in significantly improving the performance of CS. However, without accessing to the ground truth image, how to design the…
Compressed Sensing (CS) is an appealing framework for applications such as Magnetic Resonance Imaging (MRI). However, up-to-date, the sensing schemes suggested by CS theories are made of random isolated measurements, which are usually…
Compressed sensing is a new data acquisition paradigm enabling universal, simple, and reduced-cost acquisition, by exploiting a sparse signal model. Most notably, recovery of the signal by computationally efficient algorithms is guaranteed…
In compressed sensing, the restricted isometry property (RIP) on $M \times N$ sensing matrices (where $M < N$) guarantees efficient reconstruction of sparse vectors. A matrix has the $(s,\delta)$-$\mathsf{RIP}$ property if behaves as a…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy the…
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…
Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals that can be well approximated by just K << N elements from an N-dimensional basis. Instead of taking periodic…
This paper considers compressed sensing matrices and neighborliness of a centrally symmetric convex polytope generated by vectors $\pm X_1,...,\pm X_N\in\R^n$, ($N\ge n$). We introduce a class of random sampling matrices and show that they…
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. When such a signal is acquired according to the principles of CS, the measurements still…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Energy and direction are tow basic properties of a vector. A discrete signal is a vector in nature. RIP of compressive sensing can not show the direction information of a signal but show the energy information of a signal. Hence, RIP is not…
In this work, we analyze modulated sampling schemes, such as the Nyquist Folding Receiver, which are highly efficient, readily implementable, non-uniform sampling schemes that allows for the blind estimation of a narrow-band signal's…
In this paper, we aim to generalize the notion of restricted isometry constant (RIC) in compressive sensing (CS) to restricted isometry random variable (RIV). Associated with a deterministic encoder there are two RICs, namely, the left and…
Quantized compressive sensing (QCS) deals with the problem of representing compressive signal measurements with finite precision representation, i.e., a mandatory process in any practical sensor design. To characterize the signal…
In this paper, deterministic construction of measurement matrices in Compressive Sensing (CS) is considered. First, by employing the column replacement concept, a theorem for construction of large minimum distance linear codes containing…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. This paper studies a $K \times N$ partial Fourier measurement matrix for compressed sensing which is deterministically…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
Structures play a significant role in the field of signal processing. As a representative of structural data, low rank matrix along with its restricted isometry property (RIP) has been an important research topic in compressive signal…