Fast and direct inversion methods for the multivariate nonequispaced fast Fourier transform

The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various applications such as MRI, solution of PDEs, etc., are interested in the inverse problem, i.e., computing Fourier coefficients from given nonequispaced data. In this paper we survey different kinds of approaches to tackle this problem. In contrast to iterative procedures, where multiple iteration steps are needed for computing a solution, we focus especially on so-called direct inversion methods. We review density compensation techniques and introduce a new scheme that leads to an exact reconstruction for trigonometric polynomials. In addition, we consider a matrix optimization approach using Frobenius norm minimization to obtain an inverse NFFT

Optimal density compensation factors for the reconstruction of the Fourier transform of bandlimited functions

An inverse nonequispaced fast Fourier transform (iNFFT) is a fast algorithm to compute the Fourier coefficients of a trigonometric polynomial from nonequispaced sampling data. However, various applications such as magnetic resonance imaging (MRI) are concerned with the analogous problem for bandlimited functions, i.e., the reconstruction of point evaluations of the Fourier transform from given measurements of the bandlimited function. In this paper, we review an approach yielding exact reconstruction for trigonometric polynomials up to a certain degree, and extend this technique to the setting of bandlimited functions. Here we especially focus on methods computing a diagonal matrix of weights needed for sampling density compensation

Nonuniform fast Fourier transforms with nonequispaced spatial and frequency data and fast sinc transforms

In this paper we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) and the fast sinc transform as its application. The computation of NNFFT is mainly based on the nonuniform fast Fourier transform with nonequispaced spatial nodes and equispaced frequencies (NFFT). The NNFFT employs two compactly supported, continuous window functions. For fixed nonharmonic bandwidth, it is shown that the error of the NNFFT with two sinh-type window functions has an exponential decay with respect to the truncation parameters of the used window functions. As an important application of the NNFFT, we present the fast sinc transform. The error of the fast sinc transform is estimated, too

Fast and direct inversion methods for the multivariate nonequispaced fast Fourier transform

The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various applications such as MRI and solution of PDEs are interested in the inverse problem, i.e., computing Fourier coefficients from given nonequispaced data. In this article, we survey different kinds of approaches to tackle this problem. In contrast to iterative procedures, where multiple iteration steps are needed for computing a solution, we focus especially on so-called direct inversion methods. We review density compensation techniques and introduce a new scheme that leads to an exact reconstruction for trigonometric polynomials. In addition, we consider a matrix optimization approach using Frobenius norm minimization to obtain an inverse NFFT

Tissue-Specific Gene Delivery via Nanoparticle Coating

Author Manuscript: 2010 August 1.The use of biomaterials for gene delivery can potentially avoid many of the safety concerns with viral gene delivery. However, the efficacy of polymeric gene delivery methods is low, particularly in vivo. One significant concern is that the interior and exterior composition of polymeric gene delivery nanoparticles are often coupled, with a single polymer backbone governing all functions from biophysical properties of the polymer/DNA particle to DNA condensation and release. In this work we develop electrostatically adsorbed poly(glutamic acid)-based peptide coatings to alter the exterior composition of a core gene delivery particle and thereby affect tissue-specificity of gene delivery function in vivo. We find that with all coating formulations tested, the coatings reduce potential toxicity associated with uncoated cationic gene delivery nanoparticles following systemic injection. Particles coated with a low 2.5:1 peptide:DNA weight ratio (w/w) form large 2 μ sized particles in the presence of serum that can facilitate specific gene delivery to the liver. The same particles coated at a higher 20:1 w/w form small 200 nm particles in the presence of serum that can facilitate specific gene delivery to the spleen and bone marrow. Thus, variations in nanoparticle peptide coating density can alter the tissue-specificity of gene delivery in vivo.National Institutes of Health (U.S.) (BRP: 1R01CA124427-01)National Institutes of Health (U.S.) (EB 000244)National Institutes of Health (U.S.) (U54 CA119349-01)David & Lucile Packard Foundation (Fellowship 1999-1453A

A Vulnerability Assessment of Fish and Invertebrates to Climate Change on the Northeast U.S. Continental Shelf

Climate change and decadal variability are impacting marine fish and invertebrate species worldwide and these impacts will continue for the foreseeable future. Quantitative approaches have been developed to examine climate impacts on productivity, abundance, and distribution of various marine fish and invertebrate species. However, it is difficult to apply these approaches to large numbers of species owing to the lack of mechanistic understanding sufficient for quantitative analyses, as well as the lack of scientific infrastructure to support these more detailed studies. Vulnerability assessments provide a framework for evaluating climate impacts over a broad range of species with existing information. These methods combine the exposure of a species to a stressor (climate change and decadal variability) and the sensitivity of species to the stressor. These two components are then combined to estimate an overall vulnerability. Quantitative data are used when available, but qualitative information and expert opinion are used when quantitative data is lacking. Here we conduct a climate vulnerability assessment on 82 fish and invertebrate species in the Northeast U.S. Shelf including exploited, forage, and protected species. We define climate vulnerability as the extent to which abundance or productivity of a species in the region could be impacted by climate change and decadal variability. We find that the overall climate vulnerability is high to very high for approximately half the species assessed; diadromous and benthic invertebrate species exhibit the greatest vulnerability. In addition, the majority of species included in the assessment have a high potential for a change in distribution in response to projected changes in climate. Negative effects of climate change are expected for approximately half of the species assessed, but some species are expected to be positively affected (e.g., increase in productivity or move into the region). These results will inform research and management activities related to understanding and adapting marine fisheries management and conservation to climate change and decadal variability