A method to extract pure Raman spectrum of epitaxial graphene on SiC

A method is proposed to extract pure Raman spectrum of epitaxial graphene on SiC by using a Non-negative Matrix Factorization. It overcomes problems of negative spectral intensity and poorly resolved spectra resulting from a simple subtraction of a SiC background from the experimental data. We also show that the method is similar to deconvolution, for spectra composed of multiple sub- micrometer areas, with the advantage that no prior information on the impulse response functions is needed. We have used this property to characterize the Raman laser beam. The method capability in efficient data smoothing is also demonstrated.Comment: 3 figures, regular pape

Paraunitary oversampled filter bank design for channel coding

Oversampled filter banks (OSFBs) have been considered for channel coding, since their redundancy can be utilised to permit the detection and correction of channel errors. In this paper, we propose an OSFB-based channel coder for a correlated additive Gaussian noise channel, of which the noise covariance matrix is assumed to be known. Based on a suitable factorisation of this matrix, we develop a design for the decoder's synthesis filter bank in order to minimise the noise power in the decoded signal, subject to admitting perfect reconstruction through paraunitarity of the filter bank. We demonstrate that this approach can lead to a significant reduction of the noise interference by exploiting both the correlation of the channel and the redundancy of the filter banks. Simulation results providing some insight into these mechanisms are provided

Foreground separation methods for satellite observations of the cosmic microwave background

A maximum entropy method (MEM) is presented for separating the emission due to different foreground components from simulated satellite observations of the cosmic microwave background radiation (CMBR). In particular, the method is applied to simulated observations by the proposed Planck Surveyor satellite. The simulations, performed by Bouchet and Gispert (1998), include emission from the CMBR, the kinetic and thermal Sunyaev-Zel'dovich (SZ) effects from galaxy clusters, as well as Galactic dust, free-free and synchrotron emission. We find that the MEM technique performs well and produces faithful reconstructions of the main input components. The method is also compared with traditional Wiener filtering and is shown to produce consistently better results, particularly in the recovery of the thermal SZ effect.Comment: 31 pages, 19 figures (bitmapped), accpeted for publication in MNRA

3D Reconstruction of the Density Field: An SVD Approach to Weak Lensing Tomography

We present a new method for constructing three-dimensional mass maps from gravitational lensing shear data. We solve the lensing inversion problem using truncation of singular values (within the context of generalized least squares estimation) without a priori assumptions about the statistical nature of the signal. This singular value framework allows a quantitative comparison between different filtering methods: we evaluate our method beside the previously explored Wiener filter approaches. Our method yields near-optimal angular resolution of the lensing reconstruction and allows cluster sized halos to be de-blended robustly. It allows for mass reconstructions which are 2-3 orders-of-magnitude faster than the Wiener filter approach; in particular, we estimate that an all-sky reconstruction with arcminute resolution could be performed on a time-scale of hours. We find however that linear, non-parametric reconstructions have a fundamental limitation in the resolution achieved in the redshift direction.Comment: 11 pages, 6 figures. Accepted for publication in Ap