The study of sparsity has recently garnered significant attention in the signal processing and statistics communities. Generally speaking, sparsity describes the phenomenon where a large data set may be succinctly represented or approximated using only a small number of summary values or coefficients. The implications are clear—the presence of sparsity suggests the potential for efficient metho...

In compressive sensing, we want to recover a k-sparse signal x ∈ R from linear measurements of the form y = Φx, where Φ ∈ Rm×n describes the measurement process. Standard results in compressive sensing show that it is possible to exactly recover the signal x from only m = O(k log n k ) measurements for certain types of matrices. Model-based compressive sensing reduces the number of measurements...

In this paper, we consider a cognitive radio network in which energy constrained secondary users (SUs) can harvest energy from the randomly deployed power beacons (PBs). A new frame structure is proposed for the considered network. A wireless power transfer (WPT) model and a compressive spectrum sensing model are introduced. In the WPT model, a new WPT scheme is proposed, and the closed-form ex...

In wireless sensor networks (WSNs) improving the lifetime of is directly related to the energy efficiency of computation and communication operations in the sensor nodes. Compressive sensing (CS) theory suggests a new way of sensing the signal with a much lower number of linear measurements as compared to the conventional case provided that the underlying signal is sparse. This result has impli...

Compressive sensing (CS) provides an energy-efficient paradigm for data gathering in wireless sensor networks (WSNs). However, the existing work on spatial-temporal data gathering using compressive sensing only considers either multi-hop relaying based or multiple random walks based approaches. In this paper, we exploit the mobility pattern for spatial-temporal data collection and propose a nov...

One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary samples—only the sign of each linear measurement is maintained. Existing results in one-bit compressive sensing rely on the assumption that the signals of interest are s...

Compressive sensing is the newly emerging method in information technology that could impact array beamforming and the associated engineering applications. However, practical measurements are inevitably polluted by noise from external interference and internal acquisition process. Then, compressive sensing based beamforming was studied in this work for those noisy measurements with a signal-to-...

Numerous researches on Music Information Retrieval (MIR) have been estimated and linked with sparse representation method, few has paid enough attention on the application of compressive sensing and how it affects the reconstruction of MIR. This paper provides solid theoretical and various empirical evidence on the conceptualization, theoretical development, and implication of Compressive Sensi...

Recall the setup in compressive sensing. There is an unknown signal z ∈ R, and we can only glean information about z through linear measurements. We choose m linear measurements a1, . . . , am ∈ R. “Nature” then chooses a signal z, and we receive the results b1 = 〈a1, z〉, . . . , bm = 〈am, z〉 of our measurements, when applied to z. The goal is then to recover z from b. Last lecture culminated i...