Referenced compressed sensing for accurate and fast spatio-temporal signal reconstruction

We address two challenges of applying compressed sensing in a practical application, namely, its poor reconstruction quality and its high computational complexity. Since most signals are not fully sparse in practice, the reconstructed signals from conventional reconstruction methods often suffer from reconstruction artifacts due to the distortion of small coefficients. To improve the reconstruction quality, we introduce referenced compressed sensing (RefCS), a reconstruction method that exploits the spatial and/or temporal redundancy between a pair of signals. We show that using a correlated reference—an arbitrary signal close to the compressed signal—there exists the bound of reconstruction error that depends on the distance between the reference and the signal. By exploiting the correlated reference, RefCS can improve the reconstruction quality by up to 90% in terms of peak signal-to-noise ratio. Moreover, it is possible to reduce the computational complexity of the proposed RefCS using the least squares method. The least squares reconstruction results can be obtained with quality comparable to that of iterative algorithms by employing the correlated reference. Using the least squares method improves the reconstruction time by a factor in the range of 9 to 5.4  ×  10^4 according to our experiments

Mixed Compressive Sensing Back-Projection for SAR Focusing on Geocoded Grid

This article presents a new scheme called 2-D mixed compressive sensing back-projection (CS-BP-2D), for synthetic aperture radar (SAR) imaging on a geocoded grid, in a single measurement vector frame. The back-projection linear operator is derived in matrix form and a patched-based approach is proposed for reducing the dimensions of the dictionary. Spatial compressibility of the radar image is exploited by constructing the sparsity basis using the back-projection focusing framework and fast solving the reconstruction problem through the orthogonal matching pursuit algorithm. An artifact reduction filter inspired by the synthetic point spread function is used in postprocessing. The results are validated for simulated and real-world SAR data. Sentinel-1 C-band raw data in both monostatic and space-borne transmitter/stationary receiver bistatic configurations are tested. We show that CS-BP-2D can focus both monostatic and bistatic SAR images, using fewer measurements than the classical approach, while preserving the amplitude, the phase, and the position of the targets. Furthermore, the SAR image quality is enhanced and also the storage burden is reduced by storing only the recovered complex-valued points and their corresponding locations

Infrared hyperspectral imaging for point-of-care wound assessment

Wound healing assessment and management are both important in ensuring a correct healing sequence. Most of these assessment techniques involve simple observation with the naked eye, which causes two main issues: the parameters assessed are highly subjective, and they rely upon the knowledge and experience of a trained medical professional. Any failure or incorrect management can result in further complications and even fatality, therefore quantitative wound assessment techniques are the next step towards a more accessible and reliable wound management strategy. Current research in this field is focused on utilising non-invasive imaging techniques, mainly within the visible and infrared (IR) range, to identify the biological and chemical changes during the wound healing process. Any abnormalities can then be identified earlier to aid in the correct diagnosis and treatment of the wound. Technologies that utilise concepts of non-contact imaging, such as optical imaging and spectroscopy can be used to obtain spatial and spectral maps of biomarkers, which provide valuable information on the wound (e.g., precursors to improper healing or delineate viable and necrotic tissue). This work extends this research further by investigating two different imaging modalities, Negative Contrast Imaging (NCI), along with Spatial Frequency Domain Imaging (SFDI) for the applications of point of care wound assessment. Intelligent data analysis algorithms, in the form of k-means clustering and principal component analysis were applied to spectral data, collected from wound biopsies as part of a previous study, highlighting the ability to diagnose wound healing status from the contrast of spectral information, which is not reliant upon a subjective clinical diagnosis. These methods provided the motivation for a larger cell culture trauma study, in which the NCI was utilised to obtain spectral reflectance maps across a 2.5- 3.5 μm wavelength region of both healthy and traumatised human epidermal fibroblasts, induced via chemical assays. Using the same intelligent analysis tools, along with pre-processing methods including spectral derivatives, the resulting clusters can be utilised as a diagnostic tool for the assessment of cellular health and were quantifiable metrics were defined to compare the different analysis methods Near infrared (NIR) methodologies were also investigated, with two areas of SFDI identified for further advancements. Current SFDI acquisition and optical property parameter recovery is performed via a pixel-wise process, generating large amounts of data and a high computational burden for parameter recovery. Data reduction, through the application of Compressive Sensing (CS) at both the image acquisition and data analysis stages provided up to a 90% reduction in data, whilst maintaining <10% error in recovered absorption and reduced scattering optical maps. This pixel-wise methodology also affects the forward modelling and inverse problem (imaging), based upon the diffusion approximation or Monte-Carlo methods due to their pixel-independent nature. NIRFAST, an existing FEM based NIR modelling tool, was adapted to produce pixel-dependent forward modelling for heterogenic samples, providing a mechanism towards a pixel dependent SFDI image modelling and parameter recovery system

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods