Showing papers on "Fast Fourier transform published in 2010"
TL;DR: By comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces and the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.
Abstract: A new, freely available third party MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields is described. The toolbox, named k-Wave, is designed to make realistic photoacoustic modeling simple and fast. The forward simulations are based on a k-space pseudo-spectral time domain solution to coupled first-order acoustic equations for homogeneous or heterogeneous media in one, two, and three dimensions. The simulation functions can additionally be used as a flexible time reversal image reconstruction algorithm for an arbitrarily shaped measurement surface. A one-step image reconstruction algorithm for a planar detector geometry based on the fast Fourier transform (FFT) is also included. The architecture and use of the toolbox are described, and several novel modeling examples are given. First, the use of data interpolation is shown to considerably improve time reversal reconstructions when the measurement surface has only a sparse array of detector points. Second, by comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces. Last, the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.
1,629 citations
TL;DR: The icoshift program presented here is an open source and highly efficient program designed for solving signal alignment problems in metabonomic NMR data analysis and is demonstrated to be faster than similar methods found in the literature making full-resolution alignment of large datasets feasible and thus avoiding down-sampling steps such as binning.
703 citations
TL;DR: This paper proposes the use of the alternating direction method - a classic approach for optimization problems with separable variables - for signal reconstruction from partial Fourier measurements, and runs very fast (typically in a few seconds on a laptop) because it requires a small number of iterations.
Abstract: Recent compressive sensing results show that it is possible to accurately reconstruct certain compressible signals from relatively few linear measurements via solving nonsmooth convex optimization problems. In this paper, we propose the use of the alternating direction method - a classic approach for optimization problems with separable variables (D. Gabay and B. Mercier, ?A dual algorithm for the solution of nonlinear variational problems via finite-element approximations,? Computer and Mathematics with Applications, vol. 2, pp. 17-40, 1976; R. Glowinski and A. Marrocco, ?Sur lapproximation par elements finis dordre un, et la resolution par penalisation-dualite dune classe de problemes de Dirichlet nonlineaires,? Rev. Francaise dAut. Inf. Rech. Oper., vol. R-2, pp. 41-76, 1975) - for signal reconstruction from partial Fourier (i.e., incomplete frequency) measurements. Signals are reconstructed as minimizers of the sum of three terms corresponding to total variation, ?1-norm of a certain transform, and least squares data fitting. Our algorithm, called RecPF and published online, runs very fast (typically in a few seconds on a laptop) because it requires a small number of iterations, each involving simple shrinkages and two fast Fourier transforms (or alternatively discrete cosine transforms when measurements are in the corresponding domain). RecPF was compared with two state-of-the-art algorithms on recovering magnetic resonance images, and the results show that it is highly efficient, stable, and robust.
591 citations
TL;DR: The basic principles and typical applications of this technique based on grating projected and fringe analysis, which attracts the attention and research effort in the past ten years, has been targeted as main objective to review.
483 citations
TL;DR: The Hex spherical polar Fourier protein docking algorithm has been implemented on Nvidia graphics processor units (GPUs) and for the first time, exhaustive FFT-based protein docking calculations may now be performed in a matter of seconds on a contemporary GPU.
Abstract: Motivation: Modelling protein–protein interactions (PPIs) is an increasingly important aspect of structural bioinformatics. However, predicting PPIs using in silico docking techniques is computationally very expensive. Developing very fast protein docking tools will be useful for studying large-scale PPI networks, and could contribute to the rational design of new drugs.
Results: The Hex spherical polar Fourier protein docking algorithm has been implemented on Nvidia graphics processor units (GPUs). On a GTX 285 GPU, an exhaustive and densely sampled 6D docking search can be calculated in just 15 s using multiple 1D fast Fourier transforms (FFTs). This represents a 45-fold speed-up over the corresponding calculation on a single CPU, being at least two orders of magnitude times faster than a similar CPU calculation using ZDOCK 3.0.1, and estimated to be at least three orders of magnitude faster than the GPU-accelerated version of PIPER on comparable hardware. Hence, for the first time, exhaustive FFT-based protein docking calculations may now be performed in a matter of seconds on a contemporary GPU. Three-dimensional Hex FFT correlations are also accelerated by the GPU, but the speed-up factor of only 2.5 is much less than that obtained with 1D FFTs. Thus, the Hex algorithm appears to be especially well suited to exploit GPUs compared to conventional 3D FFT docking approaches.
Availability: http://hex.loria.fr/ and http://hexserver.loria.fr/
Contact: dave.ritchie@loria.fr
Supplementary information:Supplementary data are available at Bioinformatics online.
349 citations
TL;DR: A new FFT-based scheme is proposed which is as simple as the basic scheme, while remaining valid for infinite contrasts, and provides an energetically consistent rule for the homogenization of boundary voxels.
223 citations
TL;DR: Computational experiments confirm robustness of the algorithm with respect to its internal parameters and demonstrate significant increase of the convergence rate for problems with high-contrast coefficients at a low overhead per iteration.
218 citations
TL;DR: A practical scheme to perform the fast Fourier transform in the optical domain is introduced, which performs an optical real-time FFT on the consolidated OFDM data stream, thereby demultiplexing the signal into lower bit rate subcarrier tributaries, which can then be processed electronically.
Abstract: A practical scheme to perform the fast Fourier transform in the optical domain is introduced. Optical real-time FFT signal processing is performed at speeds far beyond the limits of electronic digital processing, and with negligible energy consumption. To illustrate the power of the method we demonstrate an optical 400 Gbit/s OFDM receiver. It performs an optical real-time FFT on the consolidated OFDM data stream, thereby demultiplexing the signal into lower bit rate subcarrier tributaries, which can then be processed electronically.
186 citations
TL;DR: This paper develops the first known deterministic sublinear-time sparse Fourier Transform algorithm which is guaranteed to produce accurate results and implies a simpler optimized version of the deterministic compressed sensing method previously developed in.
Abstract: We study the problem of estimating the best k term Fourier representation for a given frequency sparse signal (i.e., vector) A of length N≫k. More explicitly, we investigate how to deterministically identify k of the largest magnitude frequencies of $\hat{\mathbf{A}}$, and estimate their coefficients, in polynomial(k,log N) time. Randomized sublinear-time algorithms which have a small (controllable) probability of failure for each processed signal exist for solving this problem (Gilbert et al. in ACM STOC, pp. 152–161, 2002; Proceedings of SPIE Wavelets XI, 2005). In this paper we develop the first known deterministic sublinear-time sparse Fourier Transform algorithm which is guaranteed to produce accurate results. As an added bonus, a simple relaxation of our deterministic Fourier result leads to a new Monte Carlo Fourier algorithm with similar runtime/sampling bounds to the current best randomized Fourier method (Gilbert et al. in Proceedings of SPIE Wavelets XI, 2005). Finally, the Fourier algorithm we develop here implies a simpler optimized version of the deterministic compressed sensing method previously developed in (Iwen in Proc. of ACM-SIAM Symposium on Discrete Algorithms (SODA’08), 2008).
170 citations
TL;DR: In this article, a new time-frequency analysis method, namely, the Gabor-Wigner transform (GWT), is introduced and applied to detect and identify power quality (PQ) disturbances.
Abstract: Recently, many signal-processing techniques, such as fast Fourier transform, short-time Fourier transform, wavelet transform (WT), and wavelet packet transform (WPT), have been applied to detect, identify, and classify power-quality (PQ) disturbances. For research on PQ analysis, it is critical to apply the appropriate signal-processing techniques to solve PQ problems. In this paper, a new time-frequency analysis method, namely, the Gabor-Wigner transform (GWT), is introduced and applied to detect and identify PQ disturbances. Since GWT is an operational combination of the Gabor transform (GT) and the Wigner distribution function (WDF), it can overcome the disadvantages of both. GWT has two advantages which are that it has fewer cross-term problems than the WDF and higher clarity than the GT. Studies are presented which verify that the merits of GWT make it adequate for PQ analysis. In the case studies considered here, the various PQ disturbances, including voltage swell, voltage sag, harmonics, interharmonics, transients, voltage changes with multiple frequencies and voltage fluctuation, or flicker, will be thoroughly investigated by using this new time-frequency analysis method.
161 citations
TL;DR: This paper presents new results on an approximate Prony method (APM) which is based on [1], and applies matrix perturbation theory such that it can describe the properties and the numerical behavior of the APM in detail.
TL;DR: A robust FFT-based approach to scale-invariant image registration and introduces the normalized gradient correlation, which shows that, using image gradients to perform correlation, the errors induced by outliers are mapped to a uniform distribution for which it features robust performance.
Abstract: We present a robust FFT-based approach to scale-invariant image registration. Our method relies on FFT-based correlation twice: once in the log-polar Fourier domain to estimate the scaling and rotation and once in the spatial domain to recover the residual translation. Previous methods based on the same principles are not robust. To equip our scheme with robustness and accuracy, we introduce modifications which tailor the method to the nature of images. First, we derive efficient log-polar Fourier representations by replacing image functions with complex gray-level edge maps. We show that this representation both captures the structure of salient image features and circumvents problems related to the low-pass nature of images, interpolation errors, border effects, and aliasing. Second, to recover the unknown parameters, we introduce the normalized gradient correlation. We show that, using image gradients to perform correlation, the errors induced by outliers are mapped to a uniform distribution for which our normalized gradient correlation features robust performance. Exhaustive experimentation with real images showed that, unlike any other Fourier-based correlation techniques, the proposed method was able to estimate translations, arbitrary rotations, and scale factors up to 6.
TL;DR: In this article, an efficient implementation of the nonequilibrium Green function method combined with the density-functional theory, using localized pseudoatomic orbitals, is presented for electronic transport calculations of a system connected with two leads under a finite bias voltage.
Abstract: An efficient implementation of the nonequilibrium Green function method combined with the density-functional theory, using localized pseudoatomic orbitals, is presented for electronic transport calculations of a system connected with two leads under a finite bias voltage. In the implementation, accurate and efficient methods are developed especially for the evaluation of the density matrix and treatment of boundaries between the scattering region and the leads. Equilibrium and nonequilibrium contributions in the density matrix are evaluated with very high precision by a contour integration with a continued fraction representation of the Fermi-Dirac function and by a simple quadrature on the real axis with a small imaginary part, respectively. The Hartree potential is computed efficiently by a combination of the two-dimensional fast Fourier transform and a finite difference method, and the charge density near the boundaries is constructed with a careful treatment to avoid the spurious scattering at the boundaries. The efficiency of the implementation is demonstrated by rapid convergence properties of the density matrix. In addition, as an illustration, our method is applied for zigzag graphene nanoribbons, a Fe/MgO/Fe tunneling junction, and a ${\text{LaMnO}}_{3}/{\text{SrMnO}}_{3}$ superlattice, demonstrating its applicability to a wide variety of systems.
TL;DR: An ultra-high speed linear spline interpolation (LSI) method for λ-to-k spectral re-sampling that can be easily integrated into most ultrahigh speed FD-OCT systems to overcome the 3D data processing and visualization bottlenecks is realized.
Abstract: We realized graphics processing unit (GPU) based real-time 4D (3D+time) signal processing and visualization on a regular Fourier-domain optical coherence tomography (FD-OCT) system with a nonlinear k-space spectrometer. An ultra-high speed linear spline interpolation (LSI) method for lambda-to-k spectral re-sampling is implemented in the GPU architecture, which gives average interpolation speeds of >3,000,000 line/s for 1024-pixel OCT (1024-OCT) and >1,400,000 line/s for 2048-pixel OCT (2048-OCT). The complete FD-OCT signal processing including lambda-to-k spectral re-sampling, fast Fourier transform (FFT) and post-FFT processing have all been implemented on a GPU. The maximum complete A-scan processing speeds are investigated to be 680,000 line/s for 1024-OCT and 320,000 line/s for 2048-OCT, which correspond to 1GByte processing bandwidth. In our experiment, a 2048-pixel CMOS camera running up to 70 kHz is used as an acquisition device. Therefore the actual imaging speed is camera- limited to 128,000 line/s for 1024-OCT or 70,000 line/s for 2048-OCT. 3D Data sets are continuously acquired in real time at 1024-OCT mode, immediately processed and visualized as high as 10 volumes/second (12,500 A-scans/volume) by either en face slice extraction or ray-casting based volume rendering from 3D texture mapped in graphics memory. For standard FD-OCT systems, a GPU is the only additional hardware needed to realize this improvement and no optical modification is needed. This technique is highly cost-effective and can be easily integrated into most ultrahigh speed FD-OCT systems to overcome the 3D data processing and visualization bottlenecks.
14 Jun 2010
TL;DR: A new algorithm named SCAN (stopband cyclic algorithm new) is proposed to design unimodular sequences with spectral power suppressed in arbitrary bands and with low correlation sidelobes as well.
Abstract: One of the main objectives of cognitive radar is to adapt the spectrum of transmit waveforms to certain needs, such as avoiding reserved frequency bands or narrowband interferences. Besides spectral requirements, good correlation properties of the transmit waveforms are also desired in specific applications, such as range compression. Moreover, practical hardware constraints usually require the transmit waveforms be unimodular (i.e. only phase-modulated). In this paper, we propose a new algorithm named SCAN (stopband cyclic algorithm new) to design unimodular sequences with spectral power suppressed in arbitrary bands and with low correlation sidelobes as well. The SCAN algorithm, which starts from random initializations, can generate many sequences possessing similarly good properties. Furthermore, the SCAN algorithm is based on FFT (fast Fourier transform) operations and thus is computationally efficient, which facilitates long-sequence design and real-time waveform update.
TL;DR: A novel simplification method to reduce the hardware cost in multiplication units of the multiple-path FFT approach is proposed and a multidata scaling scheme to reduce wordlengths while preserving the signal-to-quantization-noise ratio is presented.
Abstract: This brief presents a fast Fourier transform (FFT) processor that provides high throughput rate (T.R.) by applying the eight-data-path pipelined approach for wireless personal area network applications. The hardware costs, including the power consumption and area, increase due to multiple data paths and increased wordlength along stages. To resolve these issues, a novel simplification method to reduce the hardware cost in multiplication units of the multiple-path FFT approach is proposed. A multidata scaling scheme to reduce wordlengths while preserving the signal-to-quantization-noise ratio is also presented. Using UMC 90-nm 1P9M technology, a 2048-point FFT processor test chip has been designed, and its 128-point FFT kernel has been fabricated for ultrawideband (UWB) applications and also for verification. The 2048-point FFT processor can provide a T.R. of 2.4 GS/s at 300 MHz with a power consumption of 159 mW. Compared with the four-data-path approach, a power consumption saving of about 30% can be achieved under the same T.R. In addition, the 128-point FFT kernel test chip has a measured power consumption of 6.8 mW with a T.R. of 409.6 MS/s at 52 MHz to meet the UWB standard with a saving in power consumption of about 40%.
TL;DR: In this paper, a second generation of the fast discrete curvelet transform (NFDCT) is proposed. But the second generation is lossless unlike the first generation NFDCT.
Abstract: We extend our earlier work on the nonequispaced fast discrete curvelet transform (NFDCT) and introduce a second generation of the transform. This new generation differs from the previous one by the approach taken to compute accurate curvelet coefficients from irregularly sampled data. The first generation relies on accurate Fourier coefficients obtained by an l2 -regularized inversion of the nonequispaced fast Fourier transform (FFT) whereas the second is based on a direct l1 -regularized inversion of the operator that links curvelet coefficients to irregular data. Also, by construction the second generation NFDCT is lossless unlike the first generation NFDCT. This property is particularly attractive for processing irregularly sampled seismic data in the curvelet domain and bringing them back to their irregular record-ing locations with high fidelity. Secondly, we combine the second generation NFDCT with the standard fast discrete curvelet transform (FDCT) to form a new curvelet-based method, coined noneq...
TL;DR: It is demonstrated that it is possible to straightforwardly and precisely determine the SPME parameters via the error estimates prior to the simulation for a predetermined accuracy, which can save precious computer and user time and allows an easy choice of a suitable parameter set for nearly optimal speed.
Abstract: We construct an accurate error estimate for the root mean square force error of the smooth particle mesh Ewald (SPME) algorithm, which is often used for molecular dynamics simulations, where charge configurations under periodic boundary conditions require considerable amounts of CPU time. The error estimates are provided for the ik- as well as analytical force differentiation schemes, and their validity is tested for a random homogeneous sample system. Finally, we demonstrate that it is possible to straightforwardly and precisely determine the SPME parameters via the error estimates prior to the simulation for a predetermined accuracy. This can save precious computer and user time and allows an easy choice of a suitable parameter set for nearly optimal speed.
TL;DR: A novel method to encrypt an image by multiorders of FRFT by applying the transform orders of the utilized FRFT as secret keys with a larger key space than the existing security systems based on the FRFT is proposed.
Abstract: The original information in the existing security system based on the fractional Fourier transform (FRFT) is essentially protected by only a certain order of FRFT. In this paper, we propose a novel method to encrypt an image by multiorders of FRFT. In the image encryption, the encrypted image is obtained by the summation of different orders inverse discrete FRFT of the interpolated subimages. And the original image can be perfectly recovered using the linear system constructed by the fractional Fourier domain analysis of the interpolation. The proposed method can be applied to the double or more image encryptions. Applying the transform orders of the utilized FRFT as secret keys, the proposed method is with a larger key space than the existing security systems based on the FRFT. Additionally, the encryption scheme can be realized by the fast-Fourier-transform-based algorithm and the computation burden shows a linear increase with the extension of the key space. It is verified by the experimental results that the image decryption is highly sensitive to the deviations in the transform orders.
01 Jan 2010
TL;DR: A general-purpose 2D decomposition (also known as 'pencil' or 'drawer' decomposition) communication library and a user-friendly FFT interface has been built on top of the communication library to perform distributed three-dimensional FFTs.
Abstract: As part of a HECToR distributed CSE support project, a general-purpose 2D decomposition (also known as 'pencil' or 'drawer' decomposition) communication library has been developed. This Fortran library provides a powerful and flexible framework to build applications based on 3D Cartesian data structures and spatially implicit numerical schemes (such as the compact finite difference method or spectral method). The library also supports shared-memory architecture which becomes increasingly popular. A user-friendly FFT interface has been built on top of the communication library to perform distributed three-dimensional FFTs. Both the decomposition library and the FFT interface scale well to tens of thousands of cores on Cray XT systems. The library has been applied to Incompact3D, a CFD application performing large-scale Direct Numerical Simulations of turbulence, enabling exciting scientific studies to be conducted.
TL;DR: An algorithm named EASI is presented that estimates first order sensitivity indices from given data using Fast Fourier Transformations and can be used as a post-processing module for pre-computed model evaluations.
TL;DR: The twiddle factor from the feedback in a traditional SDFT resonator is removed and thus the finite precision of its representation is no longer a problem and the accumulated errors and potential instabilities are drastically reduced in the mSDFT.
Abstract: This article presented a novel method of computing the SDFT that we call the modulated SDFT (mSDFT). The sliding discrete Fourier transform (SDFT) is a recursive algorithm that computes a DFT on a sample-by-sample basis. The accumulated errors and potential instabilities inherent in traditional SDFT algorithms are drastically reduced in the mSDFT. We removed the twiddle factor from the feedback in a traditional SDFT resonator and thus the finite precision of its representation is no longer a problem.
TL;DR: GPU-NUFFT provides an accurate approximation to GPU-NUDFT in terms of image quality, but offers >10 times higher processing speed and improved sensitivity roll-off, higher local signal-to-noise ratio and immunity to side-lobe artifacts caused by the interpolation error.
Abstract: We implemented fast Gaussian gridding (FGG)-based non-uniform fast Fourier transform (NUFFT) on the graphics processing unit (GPU) architecture for ultrahigh-speed, real-time Fourier-domain optical coherence tomography (FD-OCT). The Vandermonde matrix-based non-uniform discrete Fourier transform (NUDFT) as well as the linear/cubic interpolation with fast Fourier transform (InFFT) methods are also implemented on GPU to compare their performance in terms of image quality and processing speed. The GPU accelerated InFFT/NUDFT/NUFFT methods are applied to process both the standard half-range FD-OCT and complex full-range FD-OCT (C-FD-OCT). GPU-NUFFT provides an accurate approximation to GPU-NUDFT in terms of image quality, but offers >10 times higher processing speed. Compared with the GPU-InFFT methods, GPU-NUFFT has improved sensitivity roll-off, higher local signal-to-noise ratio and immunity to side-lobe artifacts caused by the interpolation error. Using a high speed CMOS line-scan camera, we demonstrated the real-time processing and display of GPU-NUFFT-based C-FD-OCT at a camera-limited rate of 122 k line/s (1024 pixel/A-scan).
TL;DR: In this article, a computational contact algorithm is presented to solve both the normal and tangential contact problems that describe fretting contacts between two elastic half-spaces, which is based on a conjugate gradient method and acceleration techniques based on the Fast Fourier transforms (FFT).
TL;DR: An e–cient hybrid MPI/OpenMP parallel implementation of an innovative approach that combines the Fast Fourier Transform and Multilevel Fast Multipole Algorithm has been successfully used to solve an electromagnetic problem involving 620millions of unknowns.
Abstract: MLFMA-FFT PARALLEL ALGORITHM FOR THE SO-LUTION OF LARGE-SCALE PROBLEMS IN ELECTRO-MAGNETICS (INVITED PAPER)J. M. TaboadaDepartment Tecnolog¶‡as de los Computadores y de lasComunicaciones, Escuela Polit¶ecnicaUniversidad de ExtremaduraC¶aceres 10071, SpainM. G. Araujo¶ and J. M. B¶ertoloDepartment Teor¶‡a do Sinal e Comunicaci¶ons, E.T.S.E.Telecomunicaci¶onUniversidade de VigoVigo (Pontevedra) 36310, SpainL. LandesaDepartment Tecnolog¶‡as de los Computadores y de lasComunicaciones, Escuela Polit¶ecnicaUniversidad de ExtremaduraC¶aceres 10071, SpainF. Obelleiro and J. L. RodriguezDepartment Teor¶‡a do Sinal e Comunicaci¶ons, E.T.S.E.Telecomunicaci¶onUniversidade de VigoVigo (Pontevedra) 36310, SpainAbstract|An e–cient hybrid MPI/OpenMP parallel implementationof an innovative approach that combines the Fast Fourier Transform(FFT) and Multilevel Fast Multipole Algorithm (MLFMA) has beensuccessfully used to solve an electromagnetic problem involving 620millions of unknowns. The MLFMA-FFT method can deal withextremely large problems due to its high scalability and its reducedcomputational complexity. The former is provided by the use of the
TL;DR: Simulation results show that the proposed real-time through-wall imaging algorithm with autofocusing ability in the presence of wall ambiguities can provide high-quality focused image in a short computation time regardless of the estimated value of the wall parameters.
Abstract: A novel real-time through-wall imaging (TWI) algorithm with autofocusing ability in the presence of wall ambiguities is proposed in this paper. The spectrum Green's function is employed to formulate the TWI algorithm, where the fast Fourier transform can be used to reconstruct the image in a very short computation time. The complex scattering process due to the presence of the wall is automatically included in the imaging formulation through the multilayer Green's function. The autofocusing is achieved by introducing a time factor in the TWI formulation to get a dynamic image at different focusing time. The image at the time instant when the defined entropy is minimized is stored as the output of the TWI result. Simulation results show that the proposed method can provide high-quality focused image in a short computation time regardless of the estimated value of the wall parameters.
21 Mar 2010
TL;DR: In this article, a real-time all-optical FFT receiver for OFDM data with line rates of 5.4 Tbit/s or 10.8 T bit/s is presented.
Abstract: OFDM data with line rates of 5.4 Tbit/s or 10.8 Tbit/s are generated and decoded with a new real-time all-optical FFT receiver. Each of 75 carriers of a comb source is encoded with 18 GBd QPSK or 16-QAM.
TL;DR: A novel extension of the combined Fourier-wavelet deconvolution and denoising algorithm ForWarD to the multiframe SR application that applies a space-variant nonlinear wavelet thresholding that addresses the nonstationarity inherent in resolution-enhanced fused images.
Abstract: Super-resolution (SR) is the process of combining multiple aliased low-quality images to produce a high-resolution high-quality image. Aside from registration and fusion of low-resolution images, a key process in SR is the restoration and denoising of the fused images. We present a novel extension of the combined Fourier-wavelet deconvolution and denoising algorithm ForWarD to the multiframe SR application. Our method first uses a fast Fourier-base multiframe image restoration to produce a sharp, yet noisy estimate of the high-resolution image. Our method then applies a space-variant nonlinear wavelet thresholding that addresses the nonstationarity inherent in resolution-enhanced fused images. We describe a computationally efficient method for implementing this space-variant processing that leverages the efficiency of the fast Fourier transform (FFT) to minimize complexity. Finally, we demonstrate the effectiveness of this algorithm for regular imagery as well as in digital mammography.
TL;DR: A novel computationally efficient ε-exact approximation algorithm for the univariate Gaussian kernel-based density derivative estimation that reduces the computational complexity from O(nm) to linear O(n+m) and guarantees that the actual error between the approximation and the original kernel estimate will always be less than ε.
Abstract: The computational complexity of evaluating the kernel density estimate (or its derivatives) at m evaluation points given n sample points scales quadratically as O(nm)—making it prohibitively expensive for large datasets. While approximate methods like binning could speed up the computation, they lack a precise control over the accuracy of the approximation. There is no straightforward way of choosing the binning parameters a priori in order to achieve a desired approximation error. We propose a novel computationally efficient e-exact approximation algorithm for the univariate Gaussian kernel-based density derivative estimation that reduces the computational complexity from O(nm) to linear O(n+m). The user can specify a desired accuracy e. The algorithm guarantees that the actual error between the approximation and the original kernel estimate will always be less than e. We also apply our proposed fast algorithm to speed up automatic bandwidth selection procedures. We compare our method to the best availab...
TL;DR: A novel time domain synchronisation technique is presented together with a new blind watermarking scheme which works in the discrete Fourier transform (DFT or FFT) domain, which provides excellent imperceptibility results whilst achieving robustness against typical attacks.