Narrow Results

Compressive sampling (CS) is a novel signal processing paradigm whereby the data compression is performed simultaneously with the sampling, by measuring some linear functionals of original signals in the analog domain. Once the signal is sparse sufficiently under some bases, it is strictly guaranteed to stably decompress/reconstruct the original one from significantly fewer measurements than that required by the sampling theorem, bringing considerable practical convenience. In the field of civil engineering, there are massive application scenarios for CS, as many civil engineering problems can be formulated as sparse inverse problems with linear measurements. In recent years, CS has gained extensive theoretical developments and many practical applications in civil engineering. Inevitable modelling and measurement uncertainties have motivated the Bayesian probabilistic perspective into the inverse problem of CS reconstruction. Furthermore, the advancement of deep learning techniques for efficient representation has also contributed to the elimination of the strict assumption of sparsity in CS. This paper reviews the advancements and applications of CS in civil engineering, focusing on challenges arising from data acquisition and analysis. The reviewed theories also have applicability to inverse problems in broader scientific fields.

Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows one to recover this signal from much fewer samples than the Shannon–Nyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms and others. Generally, wavelets represent point-like features while curvelets represent line-like features well. For a suitable recovery of images, we propose models that contain weighted sparsity constraints in two different frames. Given the incomplete measurements f = Φu + ϵ with the measurement matrix Φ ∈ ℝ^{K × N}, K ≪ N, we consider a jointly sparsity-constrained optimization problem of the form . Here Ψ_c and Ψ_w are the transform matrices corresponding to the two frames, and the diagonal matrices Λ_c, Λ_w contain the weights for the frame coefficients. We present efficient iteration methods to solve the optimization problem, based on Alternating Split Bregman algorithms. The convergence of the proposed iteration schemes will be proved by showing that they can be understood as special cases of the Douglas–Rachford Split algorithm. Numerical experiments for compressed sensing-based Fourier-domain random imaging show good performances of the proposed curvelet-wavelet regularized split Bregman (CWSpB) methods, where we particularly use a combination of wavelet and curvelet coefficients as sparsity constraints.

The design of a new digital radio receiver for radio astronomical observations in outer space is challenged with energy and bandwidth constraints. This paper proposes a new solution to reduce the number of samples acquired under the Shannon–Nyquist limit while retaining the relevant information of the signal. For this, it proposes to exploit the sparsity of the signal by using a compressive sampling process (also called Compressed Sensing (CS)) at the Analog-to-Digital Converter (ADC) to reduce the amount of data acquired and the energy consumption. As an example of an astrophysical signal, we have analyzed a real Jovian signal within a bandwidth of 40MHz. We have demonstrated that its best sparsity is in the frequency domain with a sparsity level of at least 10% and we have chosen, through a literature review, the Non-Uniform Sampler (NUS) as the receiver architecture. A method for evaluating the reconstruction of the Jovian signal is implemented to assess the impact of CS compression on the relevant information and to calibrate the detection threshold. Through extensive numerical simulations, and by using Orthogonal Matching Pursuit (OMP) as the reconstruction algorithm, we have shown that the Jovian signal could be sensed by taking only 20% of samples at random, while still recovering the relevant information.