Karhunen-Loeve Transform Research Articles

KLT-Based Interrogation Technique for FBG Multiplexed Sensor Tracking

The Karhunen–Loeve transform (KLT) is used to retrieve the wavelength information of several fiber Bragg gratings (FBGs) that are acting as a multiplexed sensor. The modulated light of a broadband source is launched to the FBG cascade in order to capture the electrical frequency response of the system. Thanks to dispersive media, the wavelengths of the FBGs are mapped in radio-frequency delays. Wavelength changes are determined by the amplitude change of the samples in the impulse response, a change which is followed by the eigenvalue calculated by the KLT routine. The use of the KLT routine reduces by three orders of magnitude the amount of points needed to have a subdegree resolution in temperature sensing, while keeping the accuracy almost intact.

Performance of Data Images Encryption Based Karhunen-Leoeve Transforms

The purpose of this study encryption method will apply on all parts image by the Karhunen-Loeve Transform (KLT). It will be discussed time complexity and storage complexity in method (database consists of 40 images). The Karhunen-Loeve Transform (KLT) is always used in image processing and it has a wide application area. It was called

Improved KLT Algorithm for High-Precision Wavelength Tracking of Optical Fiber Bragg Grating Sensors

Fiber Bragg Gratings (FBGs) are among the most popular optical fiber sensors. FBGs are well suited for direct detection of temperature and strain and can be functionalized for pressure, humidity, and refractive index sensing. Commercial setups for FBG interrogation are based on white-light sources and spectrometer detectors, which are capable of decoding the spectrum of an FBG array. Low-cost spectrometers record the spectrum on a coarse wavelength grid (typically 78–156 pm), whereas wavelength shifts of 1 pm or lower are required by most of the applications. Several algorithms have been presented for detection of small wavelength shift, even with coarse wavelength sampling; most notably, the Karhunen-Loeve Transform (KLT) was demonstrated. In this paper, an improved algorithm based on KLT is proposed, which is capable of further expanding the performances. Simulations show that, reproducing a commercial spectrometer with 156 pm grid, the algorithm estimates wavelength shift with accuracy well below 1 pm. In typical signal-to-noise ratio (SNR) conditions, the root mean square error is 22–220 fm, while the accuracy is 0.22 pm, despite the coarse sampling. Results have been also validated through experimental characterization. The proposed method allows achieving exceptional accuracy in wavelength tracking, beating the picometer level resolution proposed in most commercial and research software, and, due to fast operation (>5 kHz), is compatible also with structural health monitoring and acoustics.

Testing cosmological models with large-scale power modulation using microwave background polarization observations

We examine the degree to which observations of large-scale cosmic microwave background (CMB) polarization can shed light on the puzzling large-scale power modulation in maps of CMB anisotropy. We consider a phenomenological model in which the observed anomaly is caused by modulation of large-scale primordial curvature perturbations, and calculate Fisher information and error forecasts for future polarization data, constrained by the existing CMB anisotropy data. Because a significant fraction of the available information is contained in correlations with the anomalous temperature data, it is essential to account for these constraints. We also present a systematic approach to finding a set of normal modes that maximize the available information, generalizing the well-known Karhunen-Loeve transformation to take account of the constraints from the temperature data. A polarization map covering at least $\sim 60\%$ of the sky should be able to provide a $3\sigma$ detection of modulation at the level favored by the temperature data. A significant fraction of the information in such a data set is contained in the single mode that optimally encapsulates the signal due to temperature-polarization correlation.

A Hybrid Medical Image Compression Techniques for Lung Cancer

Objectives: This study focuses on Image compression and compares different methods. Methods/Statistical Analysis: In this work we simulated four image compression methods. The first method is focused on Karhunen-Loeve Transforms (KLT), second method is focused on Walsh-Hadamard Transforms (WHT), third method based on FFT and fourth one is proposed sFFT. Findings: The experimental outcomes are compared with the different quality of parameters applying on numerous lung cancers CT scan images. The Proposed SFFT method algorithm was given better results like Peak Signal to Noise Ratio (PSNR), Structural Content (SC), Mean Square Error (MSE) and Compression Ratio (CR) are compare to other Transform methods. Application /Improvement: The Proposed SFFT technique gives improved result compared with other methods in all evaluation measures.

Transmission of DWT Block-Based KLT Watermarked Images Through MC-CDMA Wireless Channel

This paper addresses the transmission of watermarked images using two watermarking methods over Multiple Carrier Code Division Multiple Access (MC-CDMA) wireless system. Both of the two proposed watermarking methods depend on combining two adequate mathematical transforms; the discrete wavelet transform (DWT) and Karhunen---Loeve Transform (KLT). The first method named DWT-based KLT watermarking embeds watermark during performing the KLT to selected middle and high frequency bands LH, HL and HH resulted from employing 2-level DWT on the cover image that will be watermarked. The second method named DWT block-based KLT watermarking works by splitting the host image into segments and each segment is subjected to 2-level DWT. Then, the watermark is embedded to every block during applying the KLT to selected middle and high frequency bands LH, HL and HH of each block separately. The watermarked images obtained by the two above mentioned watermarking methods are transmitted over the MC-CDMA wireless system. Then, the receiver manipulates the received watermarked image to extract the watermark. Experiment tests are performed and results ensure the superiority of proposed watermarking methods over the MC-CDMA with different signal-to-noise ratios.

Residual domain dictionary learning for compressed sensing video recovery

For compressed sensing (CS) recovery, the reconstruction quality is highly dependent on the sparsity level of the representation for the signal. Motivated by the observation that the temporal residual image is much sparser than its original image, a temporal residual-domain dictionary learning method for CS video recovery is proposed in this paper. The adaptive basis is learned from inter-frame differences by Karhunen---Loeve transform (KLT) to represent the residuals. And a block-based motion estimation/motion compensation (ME/MC) residual reconstruction strategy is incorporated for the CS video recovery. Experimental results on common test sequences at various sampling rates illustrate that the proposed algorithm gains great improvements over existing approaches. For some video sequences, the proposed method outperforms the state-of-art method near 1 dB in terms of peak signal noise rate (PSNR) at some higher sampling rate.

Image Steganography in a Karhunen-Loeve Transform Optimization Model

Image Steganography in a Karhunen-Loeve Transform Optimization Model

An Enhanced Hyper Spectral Image (HSI) Compression Based On Residual Dependent Arithmetic Coder (RDAC)

Background: The Hyper Spectral Image (HSI) compression is a challenging and demanding task in many remote sensing applications, because it has the large hyperspectral data. Optical remote sensing is much increased due to newly imported sensor technologies and advancements. Lossy HSI compression is an essential part for long-terms spectral storage data. In this paper, we provide a new lossy HSI compression algorithm with the help of Residual Dependent Arithmetic Coder (RDAC). Methods: The main intention of this work is to reduce the complexity while compressing the large volume of data by compressing the spectral bands. Here, the Gray Level Co-occurrence Matrix (GLCM) technique is employed to extract the texture features of the given HSI band image. Then, the k-means clustering algorithm is employed to select the reference band in each cluster based on the cluster prominence value. Moreover, the RDAC is used to compress the reference band and the residual band information of each cluster. Finally, the HSI is decompressed with the help of compressed HSI band images. Results: In experiments, the performance of the proposed method is analyzed and evaluated in terms of Mean Squared Error (MSE), Peak Signal-to-Noise Ratio (PSNR) and Compression Ratio (CR). Moreover, it is compared with some of the existing HSI compression techniques such as, Set Partitioning in Hierarchical Trees (SPIHT), Joint Photographic Expert Group (JPEG), Set Partitioning Embedded bloCK (3D-SPECK), Inverse Wavelet Transform (IWT) and Reverse Karhunen-Loeve Transform (RKLT). Conclusion: This paper proposes a new RDAC technique for lossy HSI compression. For this purpose, different image processing techniques are used. In this analysis, it is proved that the proposed HSI compression technique provides the best results, when compared to the other techniques. Keywords: 3D-SPIHT and 3D-SPECK, Bits Per Pixel (BPP), Compression Ratio (CR), Hyper Spectral Image (HSI), JPEG 2000, K-Means clustering, Mean Squared Error (MSE), Residual Dependent Arithmetic Coder (RDAC).

Use of the Karhunen–Loève Transform for interference detection and mitigation in GNSS

Abstract Improving the Global Navigation Satellite System (GNSS) receiver robustness in a radio interfered environment has been always one of the main concerns for the GNSS community. Due to the weakness of the signal impinging the GNSS receiver antenna, GNSS receiver performance can be seriously threatened by the presence of stronger interfering signals. In these scenarios, classical interference countermeasures may fail due to the fact that interference detection and removal process causes also a non-negligible degradation of the received GNSS signal. This paper introduces an innovative interference detection and mitigation technique against the well-known jamming threat. This technique is based on the use of the Karhunen–Loeve Transform (KLT) which allows for the representation of the received interfered signals in a transformed domain where interference components can be better identified, isolated and removed, avoiding significant degradation of the useful GNSS signal.

Pilot Decontamination in Wideband Massive MIMO Systems by Exploiting Channel Sparsity

This paper strives to reduce pilot contamination, a bottleneck for massive multiple-input multiple-output (MIMO) systems, by exploiting channel sparsity. Considering that typical wideband massive MIMO channel is correlated in both space and frequency domains, we employ Karhunen–Loeve Transform (KLT) and Discrete Fourier Transform (DFT) to capture the hidden sparsity of the channel. KLT basis is optimal in extracting the uncorrelated information from channel, but requires channel statistical information. As a suboptimal alternative, DFT basis can be determined without channel statistics, which is more viable for practical use. By representing the channel with DFT basis, we find that the subspaces of the desired and interference channels are approximately orthogonal, even when the number of antennas is not so large. Inspired by this observation, we propose a pilot decontamination method, where a pilot assignment policy is designed to help identify the subspace of the desired channel, and a desired channel subspace aware least square channel estimator is derived to remove the pilot contamination. The proposed method does not need channel statistics and pilot co-ordination. By exploiting channel stationary, the method does not introduce extra training overhead. Simulation results demonstrate substantial sum rate gain of the proposed method over existing methods.

Ground‐penetrating radar measurement of the distribution of thixotropic slurry behind large‐diameter segments in long‐distance pipe‐jacking construction

ABSTRACTPipe‐jacking engineering requires monitoring of the spatial distribution of thixotropic slurry behind the pipe segments, but timely thickness measurements are difficult during construction. Ground‐penetrating radar was used here during sewage pipe jacking, to evaluate the distribution of the slurry by considering its dielectric contrast with the surrounding soil. A series of circular ground‐penetrating radar data was collected along the inner surfaces of the pipe segments using an antenna with a frequency of 900 MHz. To enable accurate interpretation of the ground‐pene‐trating radar images, the dielectric parameters of the slurry were first measured by time‐domain reflectometry. Statistical analyses revealed the slurry as a special medium with extremely high dielectric constant and conductivity. Numerical simulation indicated that the ground‐penetrating radar images can be considerably improved by applying Karhunen–Loeve transformation followed by f–k Stolt migration, which facilitates identification of the reflections from the slurry–soil interface. Based on all the processed ground‐penetrating radar field data, the thickness and the distribution of the slurry at different pipe segments were calculated using the two‐way travel time and the radar signal propagation velocity in the slurry. The results show that ground‐penetrating radar is indeed effective for estimating the quality of slurry injected during pipe jacking.

ARC 2014 Over-Clocking KLT Designs on FPGAs under Process, Voltage, and Temperature Variation

Karhunen-Loeve Transformation is a widely used algorithm in signal processing that often implemented with high-throughput requisites. This work presents a novel methodology to optimise KLT designs on FPGAs that outperform typical design methodologies, through a prior characterisation of the arithmetic units in the datapath of the circuit under various operating conditions. Limited by the ever-increasing process variation, the delay models available in synthesis tools are no longer suitable for extreme performance optimisation of designs, and as they are generic, they need to consider the worst-case performance for a given fabrication process. Hence, they heavily penalise the maximum possible achieved performance of a design by leaving safety margin. This work presents a novel unified optimisation framework which contemplates a prior characterisation of the embedded multipliers on the target FPGA device under process, voltage, and temperature variation. The proposed framework allows a design space exploration leading to designs without any latency overheads that achieve high throughput while producing less errors than typical methodologies, operating with the same throughput. Experimental results demonstrate that the proposed methodology outperforms the typical implementation in three real-life design strategies: high performance, low power, and temperature variation; and it produced circuit designs that performed up to 18dB better when over-clocked.

고속 영상 압축을 위한 근사 이산 코사인 변환

ABSTRACT For image data the discrete cosine transform (DCT) has comparable energy compaction capability to Karhunen-Loeve transform (KLT) which is optimal. Hence DCT has been widely accepted in various image and video compression standard such as JPEG, MPEG-2, and MPEG-4. Recently some approximate DCT’s have been reported, which can be computed much faster than the original DCT because their coefficients are either zero or the power of 2. Although the level of energy compaction is slightly degraded, the approximate DCT’s can be utilized in real time implementation of image or visual compression applications. In this paper, an approximate 8-point DCT which contains 17 non-zero power-of-2 coefficients and high energy compaction capability comparable to DCT is proposed. Transform coding experiments with several images show that the proposed transform outperforms the published works. 키워드 : 근사 DCT, 에너지 압축, 고속 구현, 변환의 직교성 Key word : Approximate DCT, Energy compaction, High speed implementation, Orthogonality of transformsJournal of the Korea Institute of Information andCommunication Engineering

Advanced Interrogation of Fiber-Optic Bragg Grating and Fabry-Perot Sensors with KLT Analysis.

The Karhunen-Loeve Transform (KLT) is applied to accurate detection of optical fiber sensors in the spectral domain. By processing an optical spectrum, although coarsely sampled, through the KLT, and subsequently processing the obtained eigenvalues, it is possible to decode a plurality of optical sensor results. The KLT returns higher accuracy than other demodulation techniques, despite coarse sampling, and exhibits higher resilience to noise. Three case studies of KLT-based processing are presented, representing most of the current challenges in optical fiber sensing: (1) demodulation of individual sensors, such as Fiber Bragg Gratings (FBGs) and Fabry-Perot Interferometers (FPIs); (2) demodulation of dual (FBG/FPI) sensors; (3) application of reverse KLT to isolate different sensors operating on the same spectrum. A simulative outline is provided to demonstrate the KLT operation and estimate performance; a brief experimental section is also provided to validate accurate FBG and FPI decoding.

Robust Image watermarking Method Using Homomorphic Block-Based KLT

This paper introduces two robust image watermarking methods using a combination of homomorphic transform and Karhunen Loeve Transform (KLT). The first proposal is denoted as homomorphic-based KLT image watermarking. It works by inserting the watermark during applying the KLT to the reflectance component estimated from employing the homomorphic transform on the host image that will be watermarked. The reflectance component includes significant merits of image, so the embedded watermark with this component is immune to various types of attacks. The second proposal is denoted as homomorphic block-based KLT image watermarking. It works by segmenting the reflectance component of the host image into blocks using spiral scan and adding the watermark to every block during the application of the KLT to each block, separately. The watermark addition using block-by-block principle strengthens the watermark and makes it more immune to attacks. The two proposed methods are compared with homomorphic-based Singular Value Decomposition (SVD) image watermarking method, homomorphic block-based SVD image watermarking method, the traditional SVD watermarking method, and other image watermarking methods. Experimental results ensure that the two proposed methods are immune and secure to different attacks like cropping, scaling, JPEG compression and Gaussian noise without degrading the watermarked image to the same level as the other techniques.

KLT-Based Algorithm for Sub-Picometer Accurate FBG Tracking With Coarse Wavelength Sampling

An algorithm based on Karhunen–Loeve transform (KLT) for accurate tracking of fiber Bragg grating (FBG) sensors is presented. The routine is based on main eigenvalue analysis of the KLT applied to the Fourier transform of the FBG spectrum. The algorithm achieves sub-picometer accuracy, down to 4.9 fm, when applied to coarse (156 pm) wavelength sampling, providing accuracy superior to correlation-based algorithms. Experimental validation has been carried out in a climatic chamber. The proposed algorithm can be applied to any off-the-shelf white-light setup for FBG interrogation, and is compatible with 100–1-kHz operation.

A reversibility-gain model for integer Karhunen-Loève transform design in video coding

Karhunen-Loeve transform (KLT) is the optimal transform that minimizes distortion at a given bit allocation for Gaussian source. As a KLT matrix usually contains non-integers, integer-KLT design is a classical problem. In this paper, a joint reversibility-gain (R-G) model is proposed for integer-KLT design in video coding. Specifically, the ‘reversibility’ is modeled according to distortion analysis in using forward and inverse integer transform without quantization. It not only measures how invertible a transform is, but also bounds the distortion introduced by the non-orthonormal integer transform process. The ‘gain’ means transform coding gain (TCG), which is a widely used criterion for transform design in video coding. Since KLT maximizes the TCG under some assumptions, here we define the TCG loss ratio (LR) to measure how much coding gain an integer-KLT loses when compared with the original KLT. Thus, the R-G model can be explained as follows: subject to a certain TCG LR, an integer- KLT with the best reversibility is the optimal integer transform for a given non-integer-KLT. Experimental results show that the R-G model can guide the design of integer-KLTs with good performance.

A spiral based image watermarking scheme using Karhunen–Loeve and discrete hartley transforms

The main objective of developing the image watermarking technique is satisfying the robustness and the imperceptibility of multimedia protection. To achieve this objective, a novel hybrid image watermarking scheme based on Karhunen Loeve transform (KLT) and discrete hartley transform (DHT) and is proposed. In the proposed scheme (KL---DHT based watermarking scheme), the original image is divided into blocks using spiral scan, then the DHT is calculated for each block, after that, the KLT is applied for each DHT block. The watermark embedding process is carried out during the KLT transformation process. In the watermark extracting process, the watermarked image is distorted using several image attacks such as JPEG image compression, image rotation, image resizing, adding noise (Gaussian, impulsive or speckle) or image contrast adjustment using adaptive histogram equalization. Furthermore, the proposed scheme is carried out using block by block image scan and the achieved results are compared with those obtained from other watermarking schemes such as discrete cosine transform/singular value decomposition (DCT---SVD) based watermarking scheme, discrete wavelet transform/SVD (DWT---SVD) based watermarking scheme and SVD watermarking in the homomorphic domain watermarking scheme. The achieved results proved that, the superiority of the KL---DHT based watermarking scheme with spiral scan compared to other watermarking schemes in the presence of different image attacks.

Optimality of Operator-Like Wavelets for Representing Sparse AR(1) Processes

The discrete cosine transform (DCT) is known to be asymptotically equivalent to the Karhunen-Loeve transform (KLT) of Gaussian first-order auto-regressive (AR(1)) processes. Since being uncorrelated under the Gaussian hypothesis is synonymous with independence, it also yields an independent-component analysis (ICA) of such signals. In this paper, we present a constructive non-Gaussian generalization of this result: the characterization of the optimal orthogonal transform (ICA) for the family of symmetric- $\alpha$ -stable AR(1) processes. The degree of sparsity of these processes is controlled by the stability parameter $0 with the only non-sparse member of the family being the classical Gaussian AR(1) process with $\alpha=2$ . Specifically, we prove that, for $\alpha , a fixed family of operator-like wavelet bases systematically outperforms the DCT in terms of compression and denoising ability. The effect is quantified with the help of two performance criteria (one based on the Kullback-Leibler divergence, and the other on Stein’s formula for the minimum estimation error) that can also be viewed as statistical measures of independence. Finally, we observe that, for the sparser kind of processes with $0 , the operator-like wavelet basis, as dictated by linear system theory, is undistinguishable from the ICA solution obtained through numerical optimization. Our framework offers a unified view that encompasses sinusoidal transforms such as the DCT and a family of orthogonal Haar-like wavelets that is linked analytically to the underlying signal model.