Karhunen-Loeve Transform Research Articles

KLT picker: Particle picking using data-driven optimal templates

Particle picking is currently a critical step in the cryo-EM single particle reconstruction pipeline. Despite extensive work on this problem, for many data sets it is still challenging, especially for low SNR micrographs. We present the KLT (Karhunen Loeve Transform) picker, which is fully automatic and requires as an input only the approximated particle size. In particular, it does not require any manual picking. Our method is designed especially to handle low SNR micrographs. It is based on learning a set of optimal templates through the use of multi-variate statistical analysis via the Karhunen Loeve Transform. We evaluate the KLT picker on publicly available data sets and present high-quality results with minimal manual effort.

Variable Macropixel Spectral-Spatial Transforms With Intra- and Inter-Color Decorrelations for Arbitrary RGB CFA-Sampled Raw Images

A raw image captured by a color filter array (CFA), such as a Bayer pattern, is usually compressed after demosaicing with some processings (denoising, deblurring, tone-mapping, and so on). However, since photographers, designers, and high-end users prefer to work with the raw image sampled by CFA (referred to as “raw image”) directly, a raw image should be compressed before demosaicing. For effective raw image compression, this study introduces variable macropixel spectral-spatial transforms (VMSSTs), that can successfully decorrelate not only Bayer raw images but any other pure-color (RGB) ones. The proposed VMSSTs are designed by the following two steps: 1) intra-color decorrelation and 2) inter-color decorrelation. In lossless compression with JPEG 2000, compared with methods which do not use transforms, the VMSSTs reduced the average bitrates of three types of CFAs: from approximately 0.09 to 0.12 bpp for the modified Bayer CFA, from 0.25 to 0.65 bpp for the diagonal stripe CFA, and from 0.33 to 0.70 bpp for the Fujifilm X-Trans CFA due to their high color decorrelation efficiency. In addition, in lossy compression with JPEG 2000, compared with a rearranged method, the VMSSTs improved the average bitrates of the Bjontegaard delta by around 3.97%, 14.95%, and 18.65% for each CFA model, respectively. Although a data-dependent adaptive transformation, the Karhunen-Loeve transform (KLT), showed the best performance in lossy compression, the introduced VMSSTs have shown performances comparable to those of the KLT in lossless compression, despite their simple structures.

Robust multimodal biometric authentication algorithms using fingerprint, iris and voice features fusion

Development of a robust triple multimodal biometric approach for human authentication using fingerprint, iris and voice biometric is the main objective of this manuscript. Accordingly, three essential algorithms for biometric authentication are presented. The extracted features from these multimodals are combined via feature fusion center (FFC) and feature scores. These features are trained through artificial neural network (ANN) and support vector machine (SVM) classifiers. The first algorithm depends on boundary energy method (BEM) extracted features from fingerprint, normalized combinational features from iris and dimensionality reduction methods (DRM) from voice using sum/average FFC. The second proposed algorithm uses extracted features from zoning method of fingerprint, SIFT of iris and higher order statistics (HOS) of voice signals. The third proposed algorithm consists of extracted features from zoning method for fingerprint, SIFT from iris and DRM from voice signals. Classification accuracy of implemented algorithms is estimated. Comparison between proposed algorithms is introduced in terms of equal error rate (EER) and ROC curves. The experimental results confirm superiority of second proposed algorithm which achieves a classification rate of 100% using SVM classifier and sum FFC. From computational point of view, the first algorithm consumes the lowest time using SVM classifier. On other hand, the lowest EER is achieved by first proposed algorithm for extracted features from Karhunen-Loeve transform (KLT) method of DRM. Additionally, the lowest ROC curves are accomplished respectively for extracted features from multidimensional scaling (MDS), generated ARMA synthesis and Isomap features. Their accuracy is improved with SVM. Also, the sum FFC introduces efficient results compared to average FFC. These algorithms have the advantages of robustness and the strength of selecting unimodal, double and triple biometric authentication. The obtained results accomplish a remarkable accuracy for authentication and security within multi practical applications.

Graph-based Transforms for Video Coding.

In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of transforms called graph-based transforms (GBTs) for video compression, and proposes two different techniques to design GBTs. In the first technique, we formulate an optimization problem to learn graphs from data and provide solutions for optimal separable and nonseparable GBT designs, called GL-GBTs. The optimality of the proposed GL-GBTs is also theoretically analyzed based on Gaussian-Markov random field (GMRF) models for intra and inter predicted block signals. The second technique develops edge-adaptive GBTs (EA-GBTs) in order to flexibly adapt transforms to block signals with image edges (discontinuities). The advantages of EA-GBTs are both theoretically and empirically demonstrated. Our experimental results show that the proposed transforms can significantly outperform the traditional Karhunen-Loeve transform (KLT).

New signal subspace approach to estimate the inter‐area oscillatory modes in power system using TLS‐ESPRIT algorithm

The authors propose here a new low-frequency oscillatory (LFO) modes estimation scheme by applying Karhunen–Loeve transform (KLT) with total least square estimation of signal parameter employing rotational invariance technique (TLS-ESPRIT). The proposed KLT provides the perfect decorrelation of the signal from the noise at low signal-to-noise ratio and for both white and coloured noise. KLT also maximally compress the energy of the estimated signal. KLT helps to estimate the signal subspace perfectly for any non-stationary ambient power signal with the fastest computational time. First, the authors applied the KLT denoise to the filtered signal buried with highly correlated coloured Gaussian noise through the first eigenvectors of the correlation matrix and estimated the signal subspace. Finally, TLS-ESPRIT is applied to estimate the modes of the power system. A comparative analysis of the KLT-TLS-ESPRIT with the modified TLS-ESPRIT, multi-channel wavelet transform, data driven-stochastic subspace identification, TLS-ESPRIT, Root-MUSIC, and improved Prony method is presented. To explore the real-time application of the KLT-TLS-ESPRIT, the authors considered Kundur's two-area test system and 16-machine 68-bus system using 50,000 Monte-Carlo simulations. The obtained results show that the KLT-TLS-ESPRIT accurately estimates the LFO with least mean and standard deviation as compared to the remaining six methods.

Spatial correlation based channel compression feedback algorithm for massive MIMO systems

Aiming at the non-linear structure of massive multiple-input multiple-output (MIMO) channel data, this paper proposes a channel state information (CSI) compression feedback algorithm based on Laplacian Eigenmaps (LE) non-linear processing for massive MIMO uniform linear array. The spatial correlation of the channel array determines the Laplacian matrix, and the channel compression matrix is obtained by Laplacian matrix eigenvalue decomposition. The simulation results show that the proposed LE algorithm can reduce the feedback overhead, and its bit error rate (BER) performance is better than that of the discrete cosine transform (DCT) sparse compression algorithm. In addition, the proposed LE algorithm computational complexity is higher than DCT, and lower than principal component analysis (PCA) and Karhunen-Loeve transform (KLT) algorithms, but the LE algorithm can achieve higher feedback accuracy when the feedback overhead is slightly lower than DCT.

Hyperspectral image compression using hybrid transform with different wavelet-based transform coding

Hyperspectral image resolution offers limited spectral bands within a continual spectral spectrum, creating one of the spectra of most pixels inside the sequence which contains huge volume of data. Data transmission and storage is a challenging task. Compression of hyperspectral images are inevitable. This work proposes a Hyperspectral Image (HSI) compression using Hybrid Transform. First the HSI is decomposed into 1D and it is clustered and tiled. Each cluster is applied with Integer Karhunen–Loeve Transform (IKLT) and as such it is applied for whole image to get IKLT bands in spectral dimension. Then IKLT bands are applied with Integer Wavelet Transform (IDWT) to decorrelate the spatial data in spatial dimension. The combination of IKLT and IDWT is known as Hybrid transform. Second, the decorrelated wavelet coefficients are applied to Spatial-oriention Tree Wavelet (STW), Wavelet Difference Reduction (WDR) and Adaptively Scanned Wavelet Difference Reduction (ASWDR). The experimental result shows STW algorithm using Hybrid Transform gives better PSNR (db) and bits per pixel per band (bpppb) for hyperspectral images. The comparison between STW, WDR and ASWDR with Hybrid Transform for Indian Pines, Salinas, Botswana, Botswana and KSC images is experimented.

Tuning goodness-of-fit tests†

As modern precision cosmological measurements continue to show agreement with the broad features of the standard $\Lambda$-Cold Dark Matter ($\Lambda$CDM) cosmological model, we are increasingly motivated to look for small departures from the standard model's predictions which might not be detected with standard approaches. While searches for extensions and modifications of $\Lambda$CDM have to date turned up no convincing evidence of beyond-the-standard-model cosmology, the list of models compared against $\Lambda$CDM is by no means complete and is often governed by readily-coded modifications to standard Boltzmann codes. Also, standard goodness-of-fit methods such as a naive $\chi^2$ test fail to put strong pressure on the null $\Lambda$CDM hypothesis, since modern datasets have orders of magnitudes more degrees of freedom than $\Lambda$CDM. Here we present a method of tuning goodness-of-fit tests to detect potential sub-dominant extra-$\Lambda$CDM signals present in the data through compressing observations in a way that maximizes extra-$\Lambda$CDM signal variation over noise and $\Lambda$CDM variation. This method, based on a Karhunen-Loeve transformation of the data, is tuned to be maximally sensitive to particular types of variations characteristic of the tuning model; but, unlike direct model comparison, the test is also sensitive to features that only partially mimic the tuning model. As an example of its use, we apply this method in the context of a nonstandard primordial power spectrum compared against the $2015$ $Planck$ CMB temperature and polarization power spectrum. We find weak evidence of extra-$\Lambda$CDM physics, conceivably due to known systematics in the 2015 Planck polarization release.

Color PET-MRI Medical Image Fusion Combining Matching Regional Spectrum in Shearlet Domain

The color PET-MRI medical image fusion is a growing research area in medical image processing domain. MRI imagery provides the picture of the anatomy of brain tissues without any functional information, while the color PET imagery gives the functional information of brain tissues with low spatial resolution. An ideal fusion model should maintain both the functional and spatial information of the images without any spatial distortion or color deformation. In this work, we present a novel fusion technique for color PET-MRI medical images using Two-Dimensional Discrete Fourier (2DFT)-Karhunen–Loeve transform (KLT) and singular value decomposition (SVD) in shearlet domain. This method decomposes the source images into multi-scaled and multi-directional sub-bands by shearlet transform (ST). Then, SVD is utilized to eliminate superfluous ST coefficients; later, the 2DFT and KLT are utilized to estimate optimal low-pass ST coefficients in each of the decomposed images. Later, we combine the largest low-pass ST coefficients using a novel fusion strategy. The process of decomposing the source image has been discussed in detail. Finally, we use the inverse shearlet transformation (IST) to obtain the fused image. Experimental results establish the excellence of our proposed method in terms of quantitative and qualitative evaluation criteria compared to other state-of-the-art techniques.

Signal-Independent Separable KLT by Offline Training for Video Coding

After the works on High Efficiency Video Coding (HEVC) standard, the standard organizations continued to study the next generation of video coding standard, named Versatile Video Coding (VVC). The compression capacity of the VVC standard is expected to be substantially improved relative to the current HEVC standard by evolving the potential coding tools greatly. Transform is a key technique for compression efficiency, and core experiment 6 (CE6) in JVET is established to explore the transform-related coding tools. In this paper, we propose a novel signal-independent separable transform based on the Karhunen-Loeve transform (KLT) to improve the efficiency of both intra and inter residual coding. In the proposed method, the drawbacks of the traditional KLT are addressed. A group of mode-independent intra transform matrices is calculated from abundant intra residual samples of all intra modes, while the inter separable KLT matrices are trained with the residuals that cannot be efficiently processed by the discrete cosine transform type II (DCT-II). The separable KLT is developed as an additional transform type apart from DCT-II. The experimental results show that the proposed method can achieve 2.7% and 1.5% bitrate saving averagely under All Intra and Random Access configurations on top of the reference software of VVC (VTM-1.1). In addition, the consistent performance improvement on test set also validates the property of signal independency and the strong generalization capacity of the proposed separable KLT.

Joint Optimization of Transform and Quantization for High Efficiency Video Coding

In high efficiency video coding (HEVC), transformation and quantization are separately performed to eliminate the perceptual redundancy of visual signals. However, a uniform quantizer can inevitably degrade the compression efficiency of fixed transform matrices due to varying space-frequency characteristics of video content. This paper introduces a joint optimization of transform and quantization approach for video coding. First, we compute a content dependent transform from the reconstructed reference by a fast Karhunen-Loeve transform (KLT). Second, using a template-based rate regularization, we jointly optimize transform and quantization (JOTQ) as a rate constrained optimization problem and obtain a feasible solution to improve coding performance. Finally, we design fast algorithms and early terminations to reduce the computational complexity of JOTQ. The experimental results show that JOTQ outperforms several previous methods by providing Bjontegaard Delta rate reductions of 4.11% and 3.38% on average under the low-delay and random-access configuration, respectively.

Analysis of principal components used for modelling changes in glacitectonically disturbed areas

AbstractDetermination of vertical displacements of engineering objects is closely related to geodesic monitoring. Its purpose is to record the dynamics of changes in the deformation phenomenon. Geodesic monitoring requires the use of appropriate measurement equipment and appropriate methods for processing observation results, which make it possible to determine the correlation between the causes and effects of deformations in engineering objects. Progress in information technology resulted in the appearance of new methods for processing and compressing experimental data which are resistant to noise or interference and enable reduction of the amount of information.The paper presents a method for statistical analysis of multidimensional data based on PCA (principal component analysis) transformation, implemented with the use of a neural network. PCA transformation, related to the Karhunen–Loeve transformation, is used for processing signals regarded as stochastic processes. This method makes enables reduction of the input data space on the basis of independent principal components with due attention to their significance. It also makes it possible to model changes occurring in both buildings and terrain in glacitectonically disturbed areas.

An optimized non-subsampled shearlet transform-based image fusion using Hessian features and unsharp masking

Existing image fusion approaches are not so efficient to seize significant edges, texture and fine features of the source images due to ineffective and non-adaptive fusion structure. Also for objective evaluation of fusion algorithms, there is a need of a metric to measure source image features which are preserved in the fused image. To address these issues, an optimized non-subsampled shearlet transform (NSST) is developed, which is applied to decompose the source images into low- and high frequency bands. The low frequency bands are fused using proposed descriptor obtained from superposition of scale multiplied Canny edge detector features and Hessian features. The high frequency bands are fused using unsharp masking based fusion rule. Moreover, a metric QE is formulated on the basis of Karhunen-Loeve transform (KLT). The information of image pixel variance for both source and fused images can be measured by using the proposed metric QE, and it gives an indication of the amount of variance information transferred from the source images to the fused image. Both subjective and objective analysis show the efficacy of the proposed fusion structure and the metric QE.

FPGA Implementation of Optimized Karhunen–Loeve Transform for Image Processing Applications

The various transformation techniques play vital role in the field of Digital Image Processing. In this paper, we propose FPGA implementation of optimized Karhunen–Loeve transform for image processing applications. The Data Format Conversion block is introduced to represent the input data to suitable format and are fed to the Covariance computation block to calculate corresponding covariance values with accuracy. The Optimized Square Root block has been designed in the Eigenvalue computation block to obtain eigenvalues which are in turn fed to the Eigenvector computation block to produce eigenvectors using Modified divider. Further the Karhunen–Loeve Transformed matrix of the input data is obtained by performing multiplication of eigenvectors with covariance values in the matrix multiplication block. The errors are introduced due to fixed point binary calculations and are minimized by novel Error correction block. The proposed architecture is tested on Sparan-6 (XC6SLX45-3CSG324) FPGA board. The performance of the architecture is compared with respect to hardware utilization and accuracy of various existing techniques to prove the efficiency.

Algorithms for Face Image Mutual Reconstruction by Means of Two-Dimensional Projection Methods

In this paper, we consider the problem of mutual reconstruction of face image pairs. We addressed this problem in our previous article, where the proposed solutions were discussed in connection with Heterogeneous Face Recognition and Cross-Modal Multimedia Retrieval problems. Those solutions are based on one-dimensional and two-dimensional Principal Component Analysis performed over two original face images followed by their projection on independent eigenspaces, estimation of a transformation matrix and mutual reconstruction of the face image by means of one-dimensional and two-dimensional Karhunen-Loeve Transform. In this article, we propose new approaches and solutions, which are based solely on the two-dimensional eigenspace projection methods, and two regression models — Multiple Linear Regression and Partial Least Squares regression. We present the experiments on mutual reconstruction of face images in sketch/photo pairs, in pairs of face images with age-related changes, and in pairs of 2D/3D face images. In order to conduct the experiments, we selected two variants of the proposed approach. First one is based on two-dimensional Principal Component Analysis and Partial Least Squares regression, and the second one is based on two-dimensional Partial Least Squares and Multiple Linear Regression. Both variants showed acceptable performance for practical applications involving the mutual reconstruction of face images. Furthermore, we consider the method to improve the quality of reconstructed face images in the case of mixed datasets. This method involves classification of the dataset by means of two-dimensional Linear Discriminant Analysis and fitting of a separate regression model for each class. In addition, we show that generally, mutual reconstruction of face images is also achievable in conditions when original images are not a part of training sets of face images.

LeTrungThanh Optical Biosensors Based on Multimode Interference and Microring Resonator Structures

LeTrungThanh Optical Biosensors Based on Multimode Interference and Microring Resonator Structures

Structural state inspection using dual-tree quaternion wavelet transform

The dual-tree quaternion wavelet transform (QWT) was used in conjunction with quaternion-based three-channel joint transmissibility (QTJT) for state inspection. Multiple QTJTs from the same structural state were used to construct a state matrix, which was considered as a feature image. Then QWT coefficients of the feature image were calculated. It supported one magnitude and three phases, in particular, the low-frequency magnitude-phase was set as state feature index. Ultimately, the difference of the state feature indexes were utilized as the state indicator. This method reduced the influence on state inspection caused by measurement uncertainty of single testing sample, because it took overall consideration of multiple testing samples and described the similarity from multiple directions. The availability of suggested method was demonstrated by a real experiment, in which the state changing was realized by loosening fasteners and altering the longitudinal force of rail. This method was also compared with method based on Karhunen-Loeve Transform (K-LT) and artificial neural network (ANN). Experimental result indicated that the suggested method was integrated optimal, moreover, the resolution of the longitudinal force of rail was less than 10 MPa which was equivalent to temperature change of 1.75 °C for full-lock rail.

Interrogation of coarsely sampled tilted fiber Bragg grating (TFBG) sensors with KLT

Tilted fiber Bragg gratings (TFBG) can be used as refractive index sensors, as their cladding modes, amplitude, and wavelength changes with the outer refractive index. However, as cladding modes have bandwidths that are narrower than the resolution of most infrared spectrometers, they can be detected only with an optical spectrum or vector analyzers. In this work, we demonstrate that through ad hoc implementation, the Karhunen-Loeve transform (KLT) algorithm can be used to demodulate a TFBG even using a coarse interrogator (156 pm), whereas cladding modes cannot be discriminated in the TFBG spectrum. We observe that the KLT output results are a reliable indicator to detect refractive index changes up to 1.85 ⋅ 10−3 refractive index units (RIU), down to a resolution of ~10−5 RIU. The KLT can be used to demodulate TFBG sensors and biosensors operating in small refractive index change conditions.

Stochastic Elastic Properties of Composite Matrix Material with Random Voids Based on Radial Basis Function Network

The stochastic characteristics of the voids result in the randomness of the equivalent elastic modulus. It is computationally expensive to quantify the stochastic characteristics of the equivalent elastic modulus using the representative volume element. This paper is focused on the stochastic elastic properties of composite material with random voids. The Karhunen–Loeve Transform is introduced to convert the random variables to a certain number of principal components; the approximate relationship is established between the principal components and the equivalent elastic modulus taking use of the radial basis function network to reduce the computational burden. The dispersion-based sampling is proposed to solve the overfitting problem. The cumulative distribution function (CDF) and probability density function (PDF) are obtained from the surrogate model, which has good agreement with the results from Monte Carlo simulations from the original model.

A subspace based progressive coding method for speech compression

In this study, two novel methods, which are based on Karhunen Loeve Transform (KLT) and Independent Component Analysis (ICA), are proposed for coding of speech signals. Instead of immediately dealing with eigenvalue magnitudes, the KLT- and ICA-based methods use eigenvectors of covariance matrices (or independent components for ICA) by geometrically grouping these vectors into fewer numbers of vectors. In this way, a data representation compaction is achieved. Further compression is achieved through discarding autocovariance eigenvectors corresponding to the small eigenvalues and applying vector quantization on the remaining eigenvectors. Additionally, this study proposes an iterative error refinement process, which uses the rest of the available bandwidth in order to transmit an efficient representation of the description error for better SNR. The overall process constitutes a new approach to efficient speech coding, with ICA being used in subspace speech coding for the first time. Constant bit rate (CBR) and variable bit rate (VBR) coding algorithms are employed with the proposed methods. TIMIT speech database is used in the experimental studies. Speech signals are synthesized at 2.4 kbps, 8 kbps, 12.2 kbps, 16 kbps, 16.4kbps and 19.85 kbps rates by using various frame lengths. The qualities of synthesized speech signals are compared to those of available speech codecs, i.e., LPC (2.4 kbps), G.728 (LD-CELP, 16 kbps), G.729A (CS-CELP, 8 kbps), EVS (16.4 kbps), AMR-NB (12.2 kbps) and AMR-WB (19.85 kbps).