Fast Cross-correlation Research Articles

A Fast Cross-Correlation Combined with Interpolation Algorithms for the LiDAR Working in the High Background Noise

Processing speed and accuracy of measurements are important factors reflecting the performance quality of light detection and ranging (LiDAR) systems. This study proposed a fast cross-correlation (fCC) algorithm to improve the computation loading in the LiDAR system operating in high background noise environments. To reduce the calculation time, we accumulated cycles of the receiver waveform to increase the signal-to-noise ratio. In this way, the stop pulse can be easily distinguished from the background noise by applying the cross-correlation (CC) on the accumulated receiver waveform with the first start pulse. In addition, the proposed fCC combined with variant interpolation techniques: the parabolic (fCCP), gaussian (fCCG), cosine (fCCC), and cubic spline (fCCS) to increase the measurement accuracy were also investigated and compared. The experiments were performed on the real-time LiDAR system under high background light intensity. The tested results showed that the proposed method fCCP achieved 879 ns per measurement, 38 times faster than the original CC method combined with the same parabolic interpolation algorithm (CCP) 33.5 μs. Meanwhile, the fCCS method resulted in the highest accuracy/precision, reaching 5.193 cm/8.588 cm, respectively. These results demonstrated that our proposed method significantly improves the measurements speed in the LiDAR system operating under strong background light.

A Critical Comparison of Three Methods for Time-Lapse Time-Shift Calculation

Time-shift, one of the most popular time-lapse seismic attributes, has been widely used in dynamic reservoir characterization by linking it with pressure and geomechanical changes. Therefore, it is important to select appropriate calculation methods according to different time-lapse seismic data quality and time-shift magnitude. To date, there have been various published works comparing different time-shift calculation methods and discussing their advantages and disadvantages. However, most of these comparisons are based only on synthetic tests or single field applications. As the quality of time-lapse seismic data and time-shift magnitude can vary in different fields, one method may not work consistently well for each case. In this paper, a critical comparison of three different time-shift calculation techniques (Hale’s fast cross-correlation, Rickett’s non-linear inversion, and Whitcombe’s correlated leakage method) is provided. The three methods are applied to a set of synthetic data sets that are designed to account for various seismic noise and time-shift magnitudes. They are also applied to four real time-lapse seismic data sets from three North Sea fields. The calculated time-shift results are compared with the input (in synthetic tests) or the real observations from information such as seabed subsidence and compaction (in field applications). Both qualitative and quantitative comparisons are performed. At the end, each of the time-shift methods is evaluated based on different aspects, and the most appropriate method is suggested for each data scenario. All three time-shift methods are found to successfully measure time-shifts. However, Rickett’s non-linear inversion is the most outstanding method, as it gives smooth time-shifts with relatively good accuracy, and the derived time strains are more stable and interpretable.

Imaging through scattering layers exceeding memory effect range with spatial-correlation-achieved point-spread-function.

We propose to measure intensity transmission matrices or point-spread-function (PSF) of diffusers via spatial-correlation, with no scanning or interferometric detection required. With the measured PSF, we report optical imaging based on the memory effect that allows tracking of moving objects through a scattering medium. Our technique enlarges the limited effective range of traditional imaging techniques based on the memory effect, and substitutes time-consuming iterative algorithms by a fast cross-correlation deconvolution method to greatly reduce time consumption for image reconstruction.

Water Residence Time estimation by 1D deconvolution in the form of a [formula omitted]-regularized inverse problem with smoothness, positivity and causality constraints

The Water Residence Time distribution is the equivalent of the impulse response of a linear system allowing the propagation of water through a medium, e.g. the propagation of rain water from the top of the mountain towards the aquifers. We consider the output aquifer levels as the convolution between the input rain levels and the Water Residence Time, starting with an initial aquifer base level. The estimation of Water Residence Time is important for a better understanding of hydro-bio-geochemical processes and mixing properties of wetlands used as filters in ecological applications, as well as protecting fresh water sources for wells from pollutants. Common methods of estimating the Water Residence Time focus on cross-correlation, parameter fitting and non-parametric deconvolution methods. Here we propose a 1D full-deconvolution, regularized, non-parametric inverse problem algorithm that enforces smoothness and uses constraints of causality and positivity to estimate the Water Residence Time curve. Compared to Bayesian non-parametric deconvolution approaches, it has a fast runtime per test case; compared to the popular and fast cross-correlation method, it produces a more precise Water Residence Time curve even in the case of noisy measurements. The algorithm needs only one regularization parameter to balance between smoothness of the Water Residence Time and accuracy of the reconstruction. We propose an approach on how to automatically find a suitable value of the regularization parameter from the input data only. Tests on real data illustrate the potential of this method to analyze hydrological datasets.

Measurements of timing resolution of ultra-fast silicon detectors with the SAMPIC waveform digitizer

The SAMpler for PICosecond time (SAMPIC) chip has been designed by a collaboration including CEA/IRFU/SEDI, Saclay and CNRS/LAL/SERDI, Orsay. It benefits from both the quick response of a time to digital converter and the versatility of a waveform digitizer to perform accurate timing measurements. Thanks to the sampled signals, smart algorithms making best use of the pulse shape can be used to improve time resolution. A software framework has been developed to analyse the SAMPIC output data and extract timing information by using either a constant fraction discriminator or a fast cross-correlation algorithm. SAMPIC timing capabilities together with the software framework have been tested using pulses generated by a signal generator or by a silicon detector illuminated by a pulsed infrared laser. Under these ideal experimental conditions, the SAMPIC chip has proven to be capable of timing resolutions down to 4ps with synthesized signals and 40ps with silicon detector signals.

Fast cross-correlation mitigation via minimum mean-square error estimation based on matched filter outputs for consecutive DSSS signals

In the direct sequence spread spectrum (DSSS) system, multiple-access interference mitigation is critical to improving the acquisition performance. Therefore, in this paper, a fast cross-correlation mitigation algorithm based on the minimum mean-square error criterion is proposed. The algorithm exploits the matched filter outputs; hence, it is applicable to existing DSSS receivers based on direct pseudorandom noise code correlation. Essentially, the proposed scheme is an adaptive filter that optimizes each individual uncertain code phase delay. The algorithm employs both the code sequence information of the desired signal and that of the multiple-access interference signal, which enables it to outperform the standard matched filter, conventional least-mean-squares algorithm, and the pulse compression repair method. Furthermore, the proposed algorithm decreases the computational load compared with the existing multistatic adaptive pulse compression method by reducing the stage-number of the adaptive filter; this results in a slight degradation in performance. Numerical results verify the validity of the proposed algorithm.

Application of fast cross‐correlation algorithms

Cross-correlation of binary sequences is a technique used in many applications. A method is presented whereby fast cross-correlation can be employed in applications that initially use the parameters of sequences derived from difference sets. The simple idea is to replace the difference set sequence with a sequence that has similar parameters, but for which a fast cross-correlation method exists. Experimental tests using a computer confirm the time savings of this method.

Fast and sensitive rigid-body fitting into cryo-EM density maps with PowerFit

Cryo-EM is a rapidly developing method to investigate the three dimensional structure of large macromolecular complexes. In spite of all the advances in the field, the resolution of most cryo-EM density maps is too low for <em>de novo</em> model building. Therefore, the data are often complemented by fitting high-resolution subunits in the density to allow for an atomic interpretation. Typically, the first step in the modeling process is placing the subunits in the density as a rigid body. An objective method for automatic placement is full-exhaustive six dimensional cross correlation search between the model and the cryo-EM data, where the three translational and three rotational degrees of freedom are systematically sampled. In this article we present PowerFit, a Python package and program for fast and sensitive rigid body fitting. We introduce a novel, more sensitive scoring function, the core-weighted local cross correlation, and show how it can be calculated using FFTs for fast translational cross correlation scans. We further improved the search algorithm by using optimized rotational sets to reduce rotational redundancy and by limiting the cryo-EM data size through resampling and trimming the density. We demonstrate the superior scoring sensitivity of our scoring function on simulated data of the 80S D. melanogaster ribosome and on experimental data for four different cases. Through these advances, a fine-grained rotational search can now be performed within minutes on a CPU and seconds on a GPU. PowerFit is free software and can be downloaded from https://github.com/haddocking/powerfit.

Small-scale soundscapes over coral reef ecosystems: Latitudinal variation in the Northwestern Hawaiian Islands

Two-dimensional seafloor “maps” of near-field ambient sound produced by biological sources in a coral reef environment were obtained from four spur-and-groove shallow water reef environments along a latitudinal gradient in the Papahanaumokuakea Marine National Monument, Northwestern Hawaiian Islands. Acoustic data were collected in conjunction with SCUBA based ecological surveys in an effort to establish correlation between components of the acoustic field and the ecological state of each field site. Simultaneous acoustic measurements and remote underwater photographs taken during the day and at night allowed for comparisons of biological activity with recordings over time. Using a bottom-mounted L-shaped array of hydrophones, the spatial distribution, frequency, and temporal characteristics of sounds produced by small-scale biological processes were estimated within a 40 m by 40 m region around the array. A fast cross-correlation guidance technique lessened the computational burden imposed by conventional and white noise constrained adaptive focusing (curved-wavefront beamforming). Likely sources of biological sound and variation of the acoustic field within and between the sample sites will be discussed. The variation of sound field properties over latitude and correlation with ecological information obtained at each site may be useful in underwater biological surveys that utilize passive acoustic recording.

Ultrasound thermal mapping based on a hybrid method combining cross-correlation and zero-crossing tracking

A hybrid method for estimating temperature with spatial mapping using diagnostic ultrasound, based on detection of echo shifts from tissue undergoing thermal treatment, is proposed. Cross-correlation and zero-crossing tracking are two conventional algorithms used for detecting echo shifts, but their practical applications are limited. The proposed hybrid method combines the advantages of both algorithms with improved accuracy in temperature estimation. In vitro experiments were performed on porcine muscle for preliminary validation and temperature calibration. In addition, thermal mapping of rabbit thigh muscle in vivo during high-intensity focused ultrasound heating was conducted. Results from the in vitro experiments indicated that the difference between the estimated temperature change by the proposed hybrid method and the actual temperature change measured by the thermocouple was generally less than 1 °C when the increase in temperature due to heating was less than 10 °C. For the in vivo study, the area predicted to experience the highest temperature coincided well with the focal point of the high-intensity focused ultrasound transducer. The computational efficiency of the hybrid algorithm was similar to that of the fast cross-correlation algorithm, but with an improved accuracy. The proposed hybrid method could provide an alternative means for non-invasive monitoring of limited temperature changes during hyperthermia therapy.

Automatic Time Skew Detection and Correction

In this paper, we propose a new approach for the automatic time skew detection and correction for multisource audiovisual data, recorded by different cameras/recorders during the same event. All recorded data are successfully tested for potential time skew problem and corrected based on ASR-related features. The core of the algorithm is based on perceptual time-quefrency analysis with a precision of 10 ms. The results show correct time skew detection and elimination in 100% of cases for a real life dataset of 32 broken sessions and surpass the performance of fast cross correlation while keeping lower system requirements.

A Fast and Efficient Time-Delay Estimation Algorithm for Sound Localization

Time-delay estimation is an important research topic of sound localization. According to the specificity of time-delay in sound localization, a fast and efficient time-delay estimation algorithm is proposed based on the principle of fast linear cross correlation. Relative to the original time-delay estimation algorithm based on fast linear cross correlation, the proposed algorithm has enormous advantages in the time complexity and space complexity. The computing speed is twice faster than the original time-delay estimation algorithm, while the size of the memory space used is half of the original time-delay estimation algorithm.

Identification of the direction of the neural network activation with a cellular resolution by fast two-photon imaging

Spatiotemporal activity patterns in local neural networks are fundamental to understanding how information is processed and stored in brain microcircuits. Currently, imaging techniques are able to map the directional activation of macronetworks across brain areas; however, these strategies still fail to resolve the activation direction for fine microcircuits with cellular spatial resolution. Here, we show the capability to identify the activation direction of a multicell network with a cellular resolution and millisecond precision by using fast two-photon microscopy and cross correlation procedures. As an example, we characterized a directional neuronal network in an epilepsy brain slice to provide different initiation delay among multiple neurons defined at a millisecond scale.

Intra-operative ultrasound hand-held strain imaging for the visualization of ablations produced in the liver with a toroidal HIFU transducer: first in vivo results

The use of hand-held ultrasound strain imaging for the intra-operative real-time visualization of HIFU (high-intensity focused ultrasound) ablations produced in the liver by a toroidal transducer was investigated. A linear 12 MHz ultrasound imaging probe was used to obtain radiofrequency signals. Using a fast cross-correlation algorithm, strain images were calculated and displayed at 60 frames s−1, allowing the use of hand-held strain imaging intra-operatively. Fourteen HIFU lesions were produced in four pigs. Intra-operative strain imaging of HIFU ablations in the liver was feasible owing to the high frame rate. The correlation between dimensions measured on gross pathology and dimensions measured on B-mode images and on strain images were R = 0.72 and R = 0.94 respectively. The contrast between ablated and non-ablated tissue was significantly higher (p < 0.05) in the strain images (22 dB) than in the B-mode images (9 dB). Strain images allowed equivalent or improved definition of ablated regions when compared with B-mode images. Real-time intra-operative hand-held strain imaging seems to be a promising complement to conventional B-mode imaging for the guidance of HIFU ablations produced in the liver during an open procedure. These results support that hand-held strain imaging outperforms conventional B-mode ultrasound and could potentially be used for the assessment of thermal therapies.

Vehicle Flow Detection Using Fast Region Matching with Adaptive Gaussian Mixture Background Model

Video surveillance play an important role in many ITS. In this paper, we present a fast and reliable algorithm for detecting traffic flow count. The core of the algorithm relies on Gaussian mixture background model combined fast cross-correlation region-based techniques in moving object matching. By working with adaptive Gaussian mixture model, obtained the moving vehicle as foreground. Then, fast local correlation, referred to as single matching phase, is achieved by using recursive computation schemes, which enabled us to minimize the amount of calculations required at every new pixel. We have tested our match algorithm in a large set of experiments with video clips and achieved good matching results.

A Fast SEQUEST Cross Correlation Algorithm

The SEQUEST program was the first and remains one of the most widely used tools for assigning a peptide sequence within a database to a tandem mass spectrum. The cross correlation score is the primary score function implemented within SEQUEST and it is this score that makes the tool particularly sensitive. Unfortunately, this score is computationally expensive to calculate, and thus, to make the score manageable, SEQUEST uses a less sensitive but fast preliminary score and restricts the cross correlation to just the top 500 peptides returned by the preliminary score. Classically, the cross correlation score has been calculated using Fast Fourier Transforms (FFT) to generate the full correlation function. We describe an alternate method of calculating the cross correlation score that does not require FFTs and can be computed efficiently in a fraction of the time. The fast calculation allows all candidate peptides to be scored by the cross correlation function, potentially mitigating the need for the preliminary score, and enables an E-value significance calculation based on the cross correlation score distribution calculated on all candidate peptide sequences obtained from a sequence database.

A specialized fast cross-correlation for acoustical measurements using coded sequences

In acoustics applications, binary maximal-length sequences and related sequences are increasingly used for acoustics system identification tasks. A number of coded sequences, such as binary maximal-length related sequences and ternary sequences possess two-valued or pulselike autocorrelation functions. It is this correlation property that is exploited in most of acoustical applications. However, the length of some of these sequences is not directly suitable for FFT-based cross-correlation algorithms. This paper explores using standard FFTs to calculate the cross-correlation between two periodic finite-length sequences of equal length, where the lengths of the sequences are not a power of 2. We apply our specialized correlation algorithm to analyze data collected in a room-acoustic environment to simultaneously obtain impulse responses between multiple sources and multiple receivers.

Measuring Surface Topography with Scanning Electron Microscopy. I. EZEImage: A Program to Obtain 3D Surface Data

Scanning electron microscopy (SEM) is widely used in the science of materials and different parameters were developed to characterize the surface roughness. In a previous work, we studied the surface topography with fractal dimension at low scale and two parameters at high scale by using the variogram, that is, variance vs. step log-log graph, of a SEM image. Those studies were carried out with the FERImage program, previously developed by us. To verify the previously accepted hypothesis by working with only an image, it is indispensable to have reliable three-dimensional (3D) surface data. In this work, a new program (EZEImage) to characterize 3D surface topography in SEM has been developed. It uses fast cross correlation and dynamic programming to obtain reliable dense height maps in a few seconds which can be displayed as an image where each gray level represents a height value. This image can be used for the FERImage program or any other software to obtain surface topography characteristics. EZEImage also generates anaglyph images as well as characterizes 3D surface topography by means of a parameter set to describe amplitude properties and three functional indices for characterizing bearing and fluid properties.

Fast optical flow using 3D shortest path techniques

Abstract Optical flow or image motion estimation is important in the area of computer vision. This paper presents a fast and reliable optical flow algorithm which produces a dense optical flow map by using fast cross correlation and 3D shortest path techniques. Fast correlation is achieved by using the box-filtering technique which is invariant to the size of the correlation window. The motion for each scanline or each column of the input image is obtained from the correlation coefficient volume by finding the best 3D path using dynamic programming techniques rather than simply choosing the position that gives the maximum cross correlation coefficient. Sub-pixel accuracy is achieved by fitting the local correlation coefficients to a quadratic surface. Typical running time for a 256×256 image is in the order of a few seconds on a 85 MHz computer. A variety of synthetic and real images have been tested, and good results have been obtained.

Fast Stereo Matching Using Rectangular Subregioning and 3D Maximum-Surface Techniques

This paper presents a fast and reliable stereo matching algorithm which produces a dense disparity map by using fast cross correlation, rectangular subregioning (RSR) and 3D maximum-surface techniques in a coarse-to-fine scheme. Fast correlation is achieved by using the box-filtering technique whose speed is invariant to the size of the correlation window and by segmenting the stereo images into rectangular subimages at different levels of the pyramid. By working with rectangular subimages, not only can the speed of the correlation be further increased, the intermediate memory storage requirement can also be reduced. The disparity map for the stereo images is found in the 3D correlation coefficient volume by obtaining the global 3D maximum-surface rather than simply choosing the position that gives the local maximum correlation coefficient value for each pixel. The 3D maximum-surface is obtained using our new two-stage dynamic programming (TSDP) technique. There are two original contributions in this paper: (1) development of the RSR technique for fast similarity measures and (2) development of the TSDP technique for efficiently obtaining 3D maximum-surface in a 3D volume. Typical running time of our algorithm implemented in the C language on a 512 × 512 image is in the order of a few seconds on a 500 MHz PC. A variety of synthetic and real images have been tested, and good results have been obtained.