Computational Methods for Sparse Solution of Linear Inverse Problems

The goal of the sparse approximation problem is to approximate a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical engineering, statistics, and applied mathematics can be posed as sparse approximation problems, making these algorithms versatile and relevant to a plethora of applications

A unified constitutive model for asymmetric tension and compression creep-ageing behaviour of naturally aged Al-Cu-Li alloy

A set of unified constitutive equations is presented that predict the asymmetric tension and compression creep behaviour and recently observed double primary creep of pre-stretched/naturally aged aluminium-cooper-lithium alloy AA2050-T34. The evolution of the primary micro- and macro-variables related to the precipitation hardening and creep deformation of the alloy during creep age forming (CAF) are analysed and modelled. Equations for the yield strength evolution of the alloy, including an initial reversion and subsequent strengthening, are proposed based on a theory of concurrent dissolution, re-nucleation and growth of precipitates during artificial ageing. We present new observations of so-called double primary creep during the CAF process. This phenomenon is then predicted by introducing effects of interacting microstructures, including evolving precipitates, diffusing solutes and dislocations, into the sinh-law creep model. In addition, concepts of threshold creep stress σth and a microstructure-dependant creep variable H, which behave differently under different external stress directions, are proposed and incorporated into the creep model. This enables prediction of the asymmetric tension and compression creep-ageing behaviour of the alloy. Quantitative transmission electron microscopy (TEM) and related small-angle X-ray scattering (SAXS) analysis have been carried out for selected creep-aged samples to assist the development and calibration of the constitutive model. A good agreement has been achieved between the experimental results and the model. The model has the potential to be applied to creep age forming of other heat-treatable aluminium alloys

Reconstruction of compressed spectral imaging based on global structure and spectral correlation

In this paper, a convolution sparse coding method based on global structure characteristics and spectral correlation is proposed for the reconstruction of compressive spectral images. The proposed method uses the convolution kernel to operate the global image, which can better preserve image structure information in the spatial dimension. To take full exploration of the constraints between spectra, the coefficients corresponding to the convolution kernel are constrained by the norm to improve spectral accuracy. And, to solve the problem that convolutional sparse coding is insensitive to low frequency, the global total-variation (TV) constraint is added to estimate the low-frequency components. It not only ensures the effective estimation of the low-frequency but also transforms the convolutional sparse coding into a de-noising process, which makes the reconstructing process simpler. Simulations show that compared with the current mainstream optimization methods (DeSCI and Gap-TV), the proposed method improves the reconstruction quality by up to 7 dB in PSNR and 10% in SSIM, and has a great improvement in the details of the reconstructed image

4D compressive sensing holographic imaging of small moving objects with multiple illuminations

International audienceIn previous work [Opt. Lett. 44, 2827 (2019)], we presented a method based on digital holography and orthogonal matching pursuit, which is able to determine the 3D positions of small objects moving within a larger motionless object. Indeed, if the scattering density is sparse in direct 3D space, compressive sensing algorithms can be used. The method was validated by imaging red blood cell trajectories in the trunk vascular system of a zebrafish (Danio rerio) larva. We give here further details on the reconstruction technique and present a more robust version of the algorithm based on multiple illuminations