Multiresolution Estimation Research Articles

WAVELET ESTIMATION OF THE COVARIANCE OF ALMOST PERIODICALLY CORRELATED PROCESSES AND STUDY OF ASYMPTOTIC PROPERTIES IN A CONTEXT OF WEAK DEPENDENCE

We construct a multiresolution estimator and study its asymptotic properties. The estimation of the coefficients of the covariance decomposition of an almost periodically correlated process on a wavelet basis is dealt with. It is found that the covariance relates to random variables satisfying a weak dependence structure of quasi-association type. In this context, we first recall a method for constructing a wavelet base, with the decomposition of the covariance function in this base and obtain a set of coefficients to be estimated. We then construct an estimator of the coefficients obtained, under specific sampling conditions (jitter or delay). Following are the three main results obtained in the paper: • The first result concerns the almost sure convergence of the multiresolution estimator built from the model of the spectral covariance estimator. • The second result establishes consistency under the quasi-association hypothesis, a convergence rate is provided. • The third result establishes the asymptotic normality of the estimator.

CMash: fast, multi-resolution estimation of k-mer-based Jaccard and containment indices.

Motivation K-mer-based methods are used ubiquitously in the field of computational biology. However, determining the optimal value of k for a specific application often remains heuristic. Simply reconstructing a new k-mer set with another k-mer size is computationally expensive, especially in metagenomic analysis where datasets are large. Here, we introduce a hashing-based technique that leverages a kind of bottom-m sketch as well as a k-mer ternary search tree (KTST) to obtain k-mer-based similarity estimates for a range of k values. By truncating k-mers stored in a pre-built KTST with a large value, we can simultaneously obtain k-mer-based estimates for all k values up to kmax. This truncation approach circumvents the reconstruction of new k-mer sets when changing k values, making analysis more time and space-efficient.ResultsWe derived the theoretical expression of the bias factor due to truncation. And we showed that the biases are negligible in practice: when using a KTST to estimate the containment index between a RefSeq-based microbial reference database and simulated metagenome data for 10 values of k, the running time was close to 10× faster compared to a classic MinHash approach while using less than one-fifth the space to store the data structure.Availability and implementationA python implementation of this method, CMash, is available at https://github.com/dkoslicki/CMash. The reproduction of all experiments presented herein can be accessed via https://github.com/KoslickiLab/CMASH-reproducibles.Supplementary information Supplementary data are available at Bioinformatics online.

Developing and evaluating the feasibility of a new spatiotemporal fusion framework to improve remote sensing reflectance and dynamic LAI monitoring

Multi-sensor fusion provides an effective way for applications requiring remote sensing data with high spatiotemporal resolution. Especially for agricultural areas with complex planting structures and rapid changes in crop phenology, more detailed and dense time-series remote sensing data are necessary. The Sentinel-2 Multispectral Imager (S2-MSI) sensor with high spatial resolution (10–60 m) and temporal resolution (5–10 days) plays a key role in spatiotemporal fusion. But the inconsistent spatial resolution of the various bands hinders its potential application at 10 m resolution, and the multiple available fine images it provides are not fully utilized for spatiotemporal fusion. It is worth exploring how to maximize the spatial and temporal resolution of S2-MSI images to help improve the effect of spatiotemporal fusion and the dynamic monitoring of rapid crop growth. In this research, a new spatiotemporal fusion (STF) framework is developed to fuse the S2-MSI image (10 m) enhanced by Super-Resolution for multispectral Multiresolution Estimation (SupReME) algorithm and MODIS image (460 m) with a large spatial ratio (46). The proposed fusion method in the new STF framework combines the existing STF methods with Consistent Adjustment of the Climatology to Actual Observations (CACAO) algorithm, abbreviated as CA-STF. The accuracy of the fused reflectance and its capability for dynamic LAI monitoring were tested in Daman Superstation of Heihe watershed. The results indicate that: (1) the new STF framework is competent to fuse multi-source images with a ratio of 46 and outperforms the existing STF methods for both near-real-time and post-growth applications; (2) the proposed CA-STF method improves the fusion accuracy and spatial details even if only two S2-MSI images are available, especially for post-growth applications; (3) the vegetation indices (VIs) calculated from the fused images by the new STF framework provide a better correlation with LAINet measurements and improve dynamic LAI monitoring in accuracy and spatial details. This study proposes a framework to maximize the spatial and temporal resolution of S2-MSI images for spatiotemporal fusion. The synthetic daily time-series images with a high resolution of 10 m will have great potential for monitoring the dynamic changes of the land surface.

Comparison of Inversion Methods for Maize Canopy Time-Series LAI Based on SupReME Reconstructed Images

HighlightsThe Sentinel-2 images are reconstructed by the SupReME algorithm to obtain rich spatial features and consistent spectral reflectance.The reconstructed images are more advantageous for LAI estimation than the original images.The PROSAIL coupled RF model is verified to be an effective method for time-series LAI estimation at 10 m spatial resolution.Abstract. Accurate time-series crop leaf area index (LAI) monitoring can provide data support for field management and early yield estimation. The Sentinel-2 satellite has a high spatial, temporal, and spectral resolution, and its unique three red-edge bands provide an ideal data source for LAI estimation. However, the inconsistent spatial resolution of different bands hinders the application potential of Sentinel-2 images. In view of this problem, we focused on mining more information provided by the high spatial resolution bands of Sentinel-2 images using the Super-Resolution for Multispectral Multiresolution Estimation (SupReME) algorithm. Furthermore, The SNAP (Sentinel Application Platform) biophysical processor and the PROSAIL radiation transfer model coupled with Random Forest (RF) model were applied to estimate time-series LAI of maize canopy at 10 m spatial resolution, and the Leaf Area Index Wireless Sensor Network (LAINet) measurements were used for accuracy verification. Finally, the effectiveness of images reconstructed by SupReME and the two inversion methods for time-series LAI estimation were evaluated. The results showed that: (1) the Sentinel-2 images reconstructed by SupReME can improve spatial characteristics while maintaining spectral invariance, and they were more advantageous for LAI estimation than the original images; (2) The SNAP biophysical processor suits a quick large-scale estimation with robustness, while the PROSAIL coupled RF model achieved a higher coefficient of determination (R2) and a lower root mean square error (RMSE) (R2 increased by more than 0.1, RMSE decreased by more than 0.33) for time-series LAI estimation in this specific study area; (3) both inversion methods showed apparent underestimation at the late growth stage. This study verifies the feasibility of obtaining high spatial resolution images using a super-resolution algorithm for LAI inversion and provides the effect of two commonly used inversion methods for time-series LAI estimation at 10 m resolution. Keywords: Leaf area index, PROSAIL model, Random forest, SNAP biophysical processor, SupReME algorithm.

Multi-resolution estimation of the interference spectrum per pair of modes in the frequency domain.

A multi-resolution estimation method for interference spectrum separation from a one-dimensional broadband acoustic intensity is presented in this letter. The key of the proposed method is the recursion reconstruction and singular value decomposition of a 2×L Hankel matrix, which is constructed by a broadband intensity data sequence of length L + 1. Numerical simulation results show that this method can be used to achieve the zero-phase-shift estimation of each interference spectrum without any prior environmental information.

Generating Red-Edge Images at 3 M Spatial Resolution by Fusing Sentinel-2 and Planet Satellite Products

High-resolution satellite images can be used to some extent to mitigate the mixed-pixel problem caused by the lack of intensive production, farmland fragmentation, and the uneven growth of field crops in developing countries. Specifically, red-edge (RE) satellite images can be used in this context to reduce the influence of soil background at early stages as well as saturation due to crop leaf area index (LAI) at later stages. However, the availability of high-resolution RE satellite image products for research and application globally remains limited. This study uses the weight-and-unmixing algorithm as well as the SUPer-REsolution for multi-spectral Multi-resolution Estimation (Wu-SupReME) approach to combine the advantages of Sentinel-2 spectral and Planet spatial resolution and generate a high-resolution RE product. The resultant fused image is highly correlated (R2 > 0.98) with Sentinel-2 image and clearly illustrates the persistent advantages of such products. This fused image was significantly more accurate than the originals when used to predict heterogeneous wheat LAI and therefore clearly illustrated the persistence of Sentinel-2 spectral and Planet spatial advantage, which indirectly proved that the fusion methodology of generating high-resolution red-edge products from Planet and Sentinel-2 images is possible. This study provided method reference for multi-source data fusion and image product for accurate parameter inversion in quantitative remote sensing of vegetation.

DOA estimation based on multi-resolution difference co-array perspective

This paper presents two kinds of K-level co-prime linear array geometries and the corresponding direction of arrival estimation algorithm based on the multi-resolution difference co-array (MRDCA) perspective. The MRDCA can simultaneously improve the degree of freedom and the angle-resolution by utilizing a class of virtual sparse uniform linear arrays generated by vectorizing the covariance matrix of the received observations of the K-level large scale sparse array. Compared to the prior two level co-prime/nested arrays, the aperture and the angle-resolution can be significantly increased with Kth power law for the K-level array, while the dimension of its scanning space is reduced to 1/K resulted from the spatial aliasing of the MRDCA. As a result, a low-complexity DOA estimation algorithm is proposed by combining a multi-resolution estimation at each level of sparse MRDCA and a followed probability decision strategy which aims at effectively identifying the genuine DOAs and excluding the replicas. In the end, the simulation results are provided to numerically validate the performance of the proposed array geometries.

Bayesian nonparametric multiresolution estimation for the American Community Survey

Bayesian hierarchical methods implemented for small area estimation focus on reducing the noise variation in published government official statistics by borrowing information among dependent response values. Even the most flexible models confine parameters defined at the finest scale to link to each data observation in a one-to-one construction. We propose a Bayesian multiresolution formulation that utilizes an ensemble of observations at a variety of coarse scales in space and time to additively nest parameters we define at a finer scale, which serve as our focus for estimation. Our construction is motivated by and applied to the estimation of 1-year period employment totals, indexed by county, from statistics published at coarser areal domains and multi-year periods in the American Community Survey (ACS). We construct a nonparametric mixture of Gaussian processes as the prior on a set of regression coefficients of county-indexed latent functions over multiple survey years. We evaluate a modified Dirichlet process prior that incorporates county-year predictors as the mixing measure. Each county-year parameter of a latent function is estimated from multiple coarse-scale observations in space and time to which it links. The multiresolution formulation is evaluated on synthetic data and applied to the ACS.

Multi-resolution estimation of optical flow for vehicle tracking

Multi-resolution estimation of optical flow for vehicle tracking

Parallel Statistical Multiresolution Estimation for Image Reconstruction

We show that a careful parallelization of statistical multiresolution estimation (SMRE) improves the phase reconstruction in X-ray near-field holography. The central step in, and the computationally most expensive part of, SMRE methods is Dykstra's algorithm. It projects a given vector onto the intersection of convex sets. We discuss its implementation on NVIDIA's compute unified device architecture (CUDA). Compared to a CPU implementation parallelized with OpenMP, our CUDA implementation is up to one order of magnitude faster. Our results show that a careful parallelization of Dykstra's algorithm enables its use in large-scale statistical multiresolution analyses.

Robust and Fast Initialization for Intensity-Based 2D/3D Registration

Intensity-based 2D/3D registration is a key technique using digitally reconstructed radiographs (DRRs) to register the preoperative volume to the patient setup during the operation. Although DRR-based method provides a high accuracy, the small capture range hinders its clinical use. In this paper, such problem was addressed by a robust and fast initialization method using a two-level scheme including automatic tracking-based initialization (Level I) and multiresolution estimation based on central-slice theorem and phase correlation (Level II). It provided almost optimal transformation parameters for intensity-based registration. Experiments using a public gold standard data set and a spinal phantom have been conducted. The mean target registration error (mTRE) was limited in the range from 2.12 mm to 22.57 mm after tracking-based initialization. The capture range based on level II only was 20.1 mm and the mTRE in this capture range was 2.92 ± 2.21 mm. The intensity-based 2D/3D registration using proposed two-level initialization achieved the successful rate of 84.8% with the average error of 2.36 mm. The experimental results showed that the proposed method yielded the robust and fast initialization for intensity-based registration methods. In a similar way, it can be applied to other registration methods to enable a larger capture range and robust implementation.

The role of high-frequency envelope fluctuations for speech masking release

The speech-based envelope power spectrum model (sEPSM; Jo/rgensen and Dau, 2011; Jo/rgensen et al., 2013) was shown to successfully predict speech intelligibility in conditions with stationary and fluctuating interferers, reverberation, and spectral subtraction. The key element in the model was the multi-resolution estimation of the signal-to-noise ratio in the envelope domain (SNRenv) at the output of a modulation filterbank. The simulations suggested that mainly modulation filters centered in the range from 1-8 Hz contribute to speech intelligibility in the case of stationary maskers whereas modulation filters tuned to frequencies above 16 Hz might be important in the case of fluctuating maskers. In the present study, the role of high-frequency envelope fluctuations for speech masking release was further investigated in conditions of speech-on-speech Simulations were compared to various measured data from normal-hearing listeners (Festen and Plomp, 1990; Christiansen et al., 2013). The results support the hypothesis that high-frequency envelope fluctuations (>30 Hz) are essential for speech intelligibility in conditions with speech interferers. While the sEPSM reflects effects of energetic and modulation masking in speech intelligibility, the remaining unexplored effect in some conditions may be attributed to, and defined as, informational masking.

Fast Parameters Estimation of LFM Signals via Radon-Wigner Transform

The line integral of Radon-Wigner Transform (RWT) can transform the line in Wigner-Ville distribution into a point in the plane, which can be used to estimate the chirp rate and initial frequency. The calculation is costly because of two-dimensional (2-D) searching in the plane. Therefore, how to improve calculation velocity is the key of RWT method. Multi-resolution fast parameters estimation algorithm for Linear Frequency Modulation (LFM) signals via RWT is offered in this paper. The analysis results indicate that RWT is similar to Radon-ambiguity Transform (RAT) in calculation load. Performance of the parameters estimation is studied based on Residual Expansion Coefficient (REC) and Frequency Deviation Coefficient (FDC). Simulation results show that the algorithm has reached the Cramer-rao Bound (CRB) even on low SNR. The method has prospective benefits of parameters estimation for multi-component LFM signals.

Statistical Multiresolution Estimation for Variational Imaging: With an Application in Poisson-Biophotonics

In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in Frick et al. (Electron. J. Stat. 6:231---268, 2012). It constitutes a variational regularization technique that uses an ? ?-type distance measure as data-fidelity combined with a convex cost functional. The resulting convex optimization problem is approached by a combination of an inexact alternating direction method of multipliers and Dykstra's projection algorithm. We describe a novel method for balancing data-fit and regularity that is fully automatic and allows for a sound statistical interpretation. The performance of our estimation approach is studied for various problems in imaging. Among others, this includes deconvolution problems that arise in Poisson nanoscale fluorescence microscopy.

Based on the Minimum Variance Spectral Estimation of Radar Wind Profile Analysis

In this paper, we apply minimum variance method for removing automatically ground and intermittent clutter (airplane echo) from wind profiler radar data. Using the concept of discrete multi-resolution analysis and non-parametric estimation theory, we develop Doppler echo power spectral, which allow us to identify the coefficients relevant for clutter and to suppress them in order to effectively restrain and remove clutter and increase the wind profile radar detection range and accuracy; must be on the air back to the effective spectrum of the spectral moments estimation. Using MATLAB simulation analysis , compared with the conventional method of analysis to verify the feasibility and effectiveness of the algorithm, also, try the algorithm is applied to the complexity of the weather with a strong interference case of precipitation particles; Data analysis showed that the actual detection, from the library in the lower spectrum moment estimation has been improved significantly.

Bayesian hierarchical multiresolution hazard model for the study of time-dependent failure patterns in early stage breast cancer

The multiresolution estimator, developed originally in engineering applications as a wavelet-based method for density estimation, has been recently extended and adapted for estimation of hazard functions (Bouman et al. 2005, 2007). Using the multiresolution hazard (MRH) estimator in the Bayesian framework, we are able to incorporate any a priori desired shape and amount of smoothness in the hazard function. The MRH method's main appeal is in its relatively simple estimation and inference procedures, making it possible to obtain simultaneous confidence bands on the hazard function over the entire time span of interest. Moreover, these confidence bands properly reflect the multiple sources of uncertainty, such as multiple centers or heterogeneity in the patient population. Also, rather than the commonly employed approach of estimating covariate effects and the hazard function separately, the Bayesian MRH method estimates all of these parameters jointly, thus resulting in properly adjusted inference about any of the quantities.In this paper, we extend the previously proposed MRH methods (Bouman et al. 2005, 2007) into the hierarchical multiresolution hazard setting (HMRH), to accommodate the case of separate hazard rate functions within each of several strata as well as some common covariate effects across all strata while accounting for within-stratum correlation. We apply this method to examine patterns of tumor recurrence after treatment for early stage breast cancer, using data from two large-scale randomized clinical trials that have substantially influenced breast cancer treatment standards. We implement the proposed model to estimate the recurrence hazard and explore how the shape differs between patients grouped by a key tumor characteristic (estrogen receptor status) and treatment types, after adjusting for other important patient characteristics such as age, tumor size and progesterone level. We also comment on whether the hazards exhibit nonmonotonic patterns consistent with recent hypotheses suggesting multiple hazard change-points at specific time landmarks.

Estimation of the Projection Operator in a Multiresolution Multisensor Data Fusion Scheme

Zhang presented a new multiresolution multisensor data fusion scheme for dynamic systems to be observed by multisensors of different resolutions. State space projection equation is introduced to associate the states of a system at each resolution with others. A discrete model of the system is built by using Haar wavelet or general compactly supported wavelet as a linear projection operator to approximate the state space projection. In fact, different wavelet corresponds to different sensor structure. For the multiresolution multisensor system with unknown sensor structure, the projection operator should be estimated online. Up to now, this problem has never been investigated. In this brief, the projection operator is estimated by using least-square estimation algorithm and recursive least-square estimation algorithm. The research on projection operator estimation lays a foundation for the popularization and application of the multiresolution multisensor system estimation algorithm in the real system

Indoor vs. outdoor scene classification in digital photographs

This paper proposes a new technique for the classification of indoor and outdoor images based on edge analysis. Our technique is based on analysing edge straightness in images. We make an original proposal that indoor images have a greater proportion of edges that are straight compared to outdoor images, and use multi-resolution estimates on edge straightness to improve our results. We also consider this method's possible applications in a real-time system. We compare our proposed technique with a number of other approaches that have been published on indoor/outdoor classification of images and convincingly show on a large database that our method generates much higher accuracy.

Multiresolution estimates of classification complexity

In this paper, we study two measures of classification complexity based on feature space partitioning: purity and neighborhood separability. The new measures of complexity are compared with probabilistic distance measures and a number of other nonparametric estimates of classification complexity on a total of 10 databases from the University of California, Irvine, (UCI) repository.

Range image reconstruction based on robust multiresolution estimation of surface parameters

This paper proposes two robust multiresolution estimation methods of surface parameters for range images. Based on the robust estimation of surface parameters, the proposed methods approximate a patch to a planar surface in the locally adaptive window. Selection of resolution is made pixelwise by comparing a locally computed homogeneity measure with the global threshold obtained by the distribution of the approximation error. The proposed multiresolution surface parameter estimation methods are applied to range image reconstruction and segmentation. Computer simulation results with noisy images contaminated by additive Gaussian noise and impulse noise show that the proposed multiresolution reconstruction methods preserve step and roof edges better than the conventional methods. Also the segmentation methods based on the estimated surface parameters are shown to be robust to noise.