Karhunen-Loeve Transform Research Articles

Robust Watermarking Using Compressed Sensing Framework with Application to MP3 Audio

In this paper a watermark embedding and recovery technique is proposed based on the compressed sensing framework. Both the watermark and the host signal are sparse, each in its own domain. In recovery, the L1-minimization is used to recover the watermark and the host signal almost perfectly in clean conditions. The proposed technique is tested on MP3 audio compression-decompression attack and additive noise attack. Bit error rates are compared with standard spread spectrum embedding. The proposed technique is implemented for both time domain and frequency domain embedding with a unified approach. The WalshHadamard transform (WHT), the discrete cosine transform (DCT) and the Karhunen-Loeve transform (KLT) are compared in the host signal sparsifying process. Significant performance improvements in all tested conditions are achieved against the spread spectrum embedding. A payload as high as 172bps in additive noise attacks, 86bps in 128kbps MP3 attacks and 11bps in 64kbps MP3 attacks are achieved at small bit error rates and acceptable MP3 audio signal quality.

Toeplitz Approximation to Empirical Correlation Matrix of Asset Returns: A Signal Processing Perspective

Empirical correlation matrix of asset returns has its intrinsic noise component. Eigen decomposition, also called Karhunen-Loeve Transform (KLT), is employed for noise filtering where an identified subset of eigenvalues replaced by zero. The filtered correlation matrix is utilized for calculation of portfolio risk and rebalancing. We introduce Toeplitz approximation to symmetric empirical correlation matrix by using auto-regressive order one, AR(1), signal model. It leads us to an analytical framework where the corresponding eigenvalues and eigenvectors are defined in closed forms. Moreover, we show that discrete cosine transform (DCT) with implementation advantages provides comparable performance as a good approximation to KLT for processing the empirical correlation matrix of a portfolio with highly correlated assets. The energy packing of both transforms degrade for lower values of correlation coefficient. The theoretical reasoning for such a performance is presented. It is concluded that the proposed framework has a potential use for quantitative finance applications.

Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks

A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver nodes. Source nodes transmit subspace projections of random correlated signals by applying reduced-dimension linear transforms. The subspace projections are linearly processed by multiple relays and routed to intended receivers. Each receiver applies a linear estimator to approximate a subset of the sources with minimum mean squared error (MSE) distortion. The model is extended to include noisy networks with power constraints on transmitters. A key task is to compute all local compression matrices and linear estimators in the network to minimize end-to-end distortion. The non-convex problem is solved iteratively within an optimization framework using constrained quadratic programs (QPs). The proposed algorithm recovers as special cases the regular and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the distortion region of multi-source, multi-receiver networks are given for linear coding based on convex relaxations. Cut-set lower bounds are also given for any coding strategy based on information theory. The distortion region and compression-estimation tradeoffs are illustrated for different communication demands (e.g. multiple unicast), and graph structures.

De-noising of dynamic magnetic resonance images by the combined application of wavelet filtering and Karhunen-Loeve Transform (KLT)

Methods The proposed approach combines 2D spatial wavelet filtering with 1D temporal Karhunen-Loeve Transform (KLT). The KLT is first applied to create a series of “eigenimages” in which important signal information is concentrated into only a few eigenimages. Then a 2D spatial wavelet filter is applied to each of the individual eigenimages. An adaptive threshold is used to define the wavelet filter strength for each of the eigenimages based on the noise variance and standard deviation of the signal, resulting in stronger filtering of the eigenimages that primarily contain noise. After wavelet filtering, the de-noised eigenimages are transformed back into image space. The performance of this filtering approach was tested over a range of wavelet filter strengths (1x to 4x adaptive threshold) for noise reduction and edge sharpness in a digital phantom. SNR improvement was also evaluated in real-time stress cine image series acquired in five normal volunteers. SNR was calculated in phantom and human images by finding the mean signal value and noise variance in a region-of-interest (ROI) within each frame. The sharpness in phantom images was measured as the distance between 20% and 80% of the total rise/fall for a moving edge.

Application of the Karhunen-Loeve transformation in bio-radiolocation: Breath simulation

An application of the Karhunen-Loeve transformation (principal component analysis) to the extraction of the signal corresponding to small breathing displacements of the human chest is illustrated by the example of the ultrabandwidth impulse reflected from a simple human target. The reduction in the dimensions of the original signals from 256 to 5 is shown by experiments to take place in the case of small displacements and the mean-square error not exceeding 10%.

Non-rigid registration and KLT filter to improve SNR and CNR in GRE-EPI myocardial perfusion imaging.

The purpose of the study was to evaluate the effect of motion compensation by non-rigid registration combined with the Karhunen-Loeve Transform (KLT) filter on the signal to noise (SNR) and contrast-to-noise ratio (CNR) of hybrid gradient-echo echoplanar (GRE-EPI) first-pass myocardial perfusion imaging. Twenty one consecutive first-pass adenosine stress perfusion MR data sets interpreted positive for ischemia or infarction were processed by non-rigid Registration followed by KLT filtering. SNR and CNR were measured in abnormal and normal myocardium in unfiltered and KLT filtered images following non-rigid registration to compensate for respiratory and other motions. Image artifacts introduced by filtering in registered and nonregistered images were evaluated by two observers. There was a statistically significant increase in both SNR and CNR between normal and abnormal myocardium with KLT filtering (mean SNR increased by 62.18% ± 21.05% and mean CNR increased by 58.84% ± 18.06%; p = 0.01). Motion correction prior to KLT filtering reduced significantly the occurrence of filter induced artifacts (KLT only-artifacts in 42 out of 55 image series vs. registered plus KLT-artifacts in 3 out of 55 image series). In conclusion the combination of non- rigid registration and KLT filtering was shown to increase the SNR and CNR of GRE-EPI perfusion images. Subjective evaluation of image artifacts revealed that prior motion compensation significantly reduced the artifacts introduced by the KLT filtering process.

A DCT-Based Speech Enhancement System With Pitch Synchronous Analysis

Discrete cosine transform (DCT) has been proven to be a good approximation to the Karhunen-Loeve Transform (KLT) and has similar properties to the discrete Fourier transform (DFT). It also possesses a better energy compaction capability which is advantageous for speech enhancement. However, frame to frame variations of DCT coefficients even for a perfectly stationary signal can be observed. Therefore a DCT-based speech enhancement system with pitch synchronous analysis is proposed to overcome this problem. It reduces the drawbacks of fixed window shift and the amount of shift in the analysis window is now based on the pitch period, thus increasing the inter-frame similarities. Furthermore, a Wiener filter using the a priori signal-to-noise ratio (SNR) with an adaptive parameter is also derived and implemented as an advanced noise reduction filter. This proposed speech enhancement system is evaluated in terms of several objective measures and the experimental results demonstrate the good performance of the proposed system.

A Novel Image Signature Method for Content Authentication

We proposed an image signature method for content authentication, which applies a hierarchical approach to construct an image signature. In the first level, DWT and DCT are used to extract image features; then these features are encrypted by using sub-keys that are generated by a cryptographically hash function. In the second level, Karhunen–Loeve transformation is used to reduce the signature length. The main features of the proposed method are as follows: (i) It achieves a trade-off between robustness and tampering sensitivity. (ii) It provides a tool for image tampering detection and tampering localization. (iii) It can be used to detect the thumbnail of the large image to improve detection efficiency. (iv) It provides the compact signature, and the signature length is independent of the image size. Experimental results show that proposed method is robust for content-preserving manipulations such as JPEG compression, adding noise, filtering and Gamma correction, etc.

Jointly Optimized Spatial Prediction and Block Transform for Video and Image Coding

This paper proposes a novel approach to jointly optimize spatial prediction and the choice of the subsequent transform in video and image compression. Under the assumption of a separable first-order Gauss-Markov model for the image signal, it is shown that the optimal Karhunen-Loeve Transform, given available partial boundary information, is well approximated by a close relative of the discrete sine transform (DST), with basis vectors that tend to vanish at the known boundary and maximize energy at the unknown boundary. The overall intraframe coding scheme thus switches between this variant of the DST named asymmetric DST (ADST), and traditional discrete cosine transform (DCT), depending on prediction direction and boundary information. The ADST is first compared with DCT in terms of coding gain under ideal model conditions and is demonstrated to provide significantly improved compression efficiency. The proposed adaptive prediction and transform scheme is then implemented within the H.264/AVC intra-mode framework and is experimentally shown to significantly outperform the standard intra coding mode. As an added benefit, it achieves substantial reduction in blocking artifacts due to the fact that the transform now adapts to the statistics of block edges. An integer version of this ADST is also proposed.

Reduced order optimization for model predictive control using principal control moves

In order to reduce the computational complexity of model predictive control (MPC) a proper input signal parametrization is proposed in this paper which significantly reduces the number of decision variables. This parametrization can be based on either measured data from closed-loop operation or simulation data. The snapshots of representative time domain data for all manipulated variables are projected on an orthonormal basis by a Karhunen–Loeve transformation. These significant features (termed principal control moves, PCM) can be reduced utilizing an analytic criterion for performance degradation. Furthermore, a stability analysis of the proposed method is given. Considerations on the identification of the PCM are made and another criterion is given for a sufficient selection of PCM. It is shown by an example of an industrial drying process that a strong reduction in the order of the optimization is possible while retaining a high performance level.

Low-Complexity Hyperspectral Image Coding Using Exogenous Orthogonal Optimal Spectral Transform (OrthOST) and Degree-2 Zerotrees

We introduce a low-complexity codec for lossy compression of hyperspectral images. These images have two kinds of redundancies: 1) spatial; and 2) spectral. Our coder is based on a compression scheme consisting in applying a 2-D discrete wavelet transform (DWT) to each component and a linear transform between components to reduce, respectively, spatial and spectral redundancies. The DWT used is the Daubechies 9/7. However, the spectral transform depends on the spectrometer sensor and the kind of images to be encoded. It is calculated once and for all on a set of images (the learning basis) from (only) one sensor, thanks to Akam Bita et al. 's OrthOST algorithm that returns an orthogonal spectral transform, whose optimality in high-rate coding has been recently proved under mild conditions. The spectral transform obtained in this way is applied to encode other images from the same sensor. Quantization and entropy coding are then achieved with a well-suited extension to hyperspectral images of the Said and Pearlman's SPIHT algorithm. Comparisons with a JPEG2000 codec using the Karhunen-Loeve transform (KLT) to reduce spectral redundancy show good performance for our codec.

Improved real-time blood flow velocity quantification via application of the Karhunen-Loeve transform for increased signal-to-noise ratio

Background Real-time blood flow velocity quantification requires fast acquisition time and both high spatial and temporal resolution in order to capture clinically relevant features. Multi-coil parallel imaging techniques trade fast realtime cine acquisition with high temporal resolution for lower signal quality. Methods for increasing signal-tonoise ratio (SNR) will allow higher acceleration rates in parallel imaging, leading to faster acquisition times in the context of exercise stress while maintaining signal quality. Increased SNR via the Karhunen-Loeve Transform [1] (KLT) is achieved by decomposing a temporal cine sequence into a series of eigenmodes where the signal of interest is localized in a subset of eigenmodes and eliminating noise-only eigenmodes.

Astronomical Image Compression Techniques Based on ACC and KLT Coder

This paper deals with a compression of image data in applications in astronomy. Astronomical images have typical specific properties — high grayscale bit depth, size, noise occurrence and special processing algorithms. They belong to the class of scientific images. Their processing and compression is quite different from the classical approach of multimedia image processing. The database of images from BOOTES (Burst Observer and Optical Transient Exploring System) has been chosen as a source of the testing signal. BOOTES is a Czech-Spanish robotic telescope for observing AGN (active galactic nuclei) and the optical transient of GRB (gamma ray bursts) searching. This paper discusses an approach based on an analysis of statistical properties of image data. A comparison of two irrelevancy reduction methods is presented from a scientific (astrometric and photometric) point of view. The first method is based on a statistical approach, using the Karhunen-Loeve transform (KLT) with uniform quantization in the spectral domain. The second technique is derived from wavelet decomposition with adaptive selection of used prediction coefficients. Finally, the comparison of three redundancy reduction methods is discussed. Multimedia format JPEG2000 and HCOMPRESS, designed especially for astronomical images, are compared with the new Astronomical Context Coder (ACC) coder based on adaptive median regression.

All-optical KarhunenLoeve Transform Using Multimode Interference Structures on Silicon Nanowires

A variety of unitary transforms have attracted considerable attention for their application in data, image compression and other signal processing applications. Among many transforms, the KarhunenLoeve transform (KLT) is known to be optimal because of its advantages of computational efficiency, residual correlation and rate distortion criterion. In this paper, it is shown that the all-optical KarhunenLoeve transform can be realized using multimode interference (MMI) structures on silicon wire waveguides. The transfer matrix method (TMM) and the beam propagation method (BPM) are used to verify and optimally design the proposed devices.

Gaussian Mixture Model-based Quantization of Line Spectral Frequencies for Adaptive Multirate Speech Codec

In this paper, we investigate the use of a Gaussian MixtureModel (GMM)-based quantizer for quantization of the Line Spectral Frequencies (LSFs) in the Adaptive Multi-Rate (AMR) speech codec. We estimate the parametric GMM model of the probability density function (pdf) for the prediction error (residual) of mean-removed LSF parameters that are used in the AMR codec for speech spectral envelope representation. The studied GMM-based quantizer is based on transform coding using Karhunen-Loeve transform (KLT) and transform domain scalar quantizers (SQ) individually designed for each Gaussian mixture. We have investigated the applicability of such a quantization scheme in the existing AMR codec by solely replacing the AMR LSF quantization algorithm segment. The main novelty in this paper lies in applying and adapting the entropy constrained (EC) coding for fixed-rate scalar quantization of transformed residuals thereby allowing for better adaptation to the local statistics of the source. We study and evaluate the compression efficiency, computational complexity and memory requirements of the proposed algorithm. Experimental results show that the GMM-based EC quantizer provides better rate/distortion performance than the quantization schemes used in the referent AMR codec by saving up to 7.32 bits/frame at much lower rate-independent computational complexity and memory requirements.

Dimethylglyoxime (DMG) staining for semi-quantitative mapping of Ni in plant tissue

Determination of the nickel (Ni) distribution in tissues of hyperaccumulator plants aids in understanding the strategies and mechanisms used by these plants to take up Ni from soils. Commonly used methods for measuring Ni distribution in plant tissues require expensive equipment and complex sample preparation. We tested a suite of staining methods consisting of dimethylglyoxime (DMG) dissolved in a range of solvents for the mapping of Ni distribution in the Ni hyperaccumulator Berkheya coddii Roessler. The best solution was DMG (10gl−1) dissolved in borax (25mM) and KOH (30mM). Plant tissue cross-sections were imaged under a microscope immediately after DMG application. A Karhunen–Loeve transformation was applied to the images to minimize interference from colours of other origin, e.g. from chlorophyll. The distribution of Ni could be determined at the cellular level and consistent patterns were obtained for replicates. Staining of Ni dissolved in agar at various concentrations was used to calibrate the method. Concentrations as low as 50mgkg−1 (fresh weight) could be detected. Averaged over several cross-sections the DMG method systematically gave lower concentrations than ICP-OES analysis of the respective plant part, indicating that not all Ni in the tissue reacted with DMG, but only Ni that is readily available. The DMG method may be used in conjunction with spectroscopic methods to resolve biologically active Ni.

Medical image registration using modified iterative closest points

The closest iterative point (ICP) algorithm is commonly used in medical image registration. However, due to its natural limitation, the processing time and registration accuracy need to be further advanced. In this paper, by computing the moments of the reference and floating images, the centroids are computed and thus the initial translation parameters are obtained. The rotation angles acquired respectively by the second-order central moments, inertia matrix, Karhunen–Loeve transformation (K-LT) and singular value decomposition (SVD) are referred to as the initial rotation parameters of the ICP algorithm for image registration. The edges of the reference and floating images are detected by Canny operator and then the binarization images involving the feature points are acquired. The experimental results show that this proposed method has a fairly simple implementation, a low computational load, a fast registration and good registration accuracy. It also can efficiently avoid trapping into the local optimum and is adapted for both mono-modality and multi-modality image registrations. Copyright © 2010 John Wiley & Sons, Ltd.

SISTEM PENGENALAN WAJAH 3-D MENGGUNAKAN PENAMBAHAN GARIS CIRI PADA METODE PERHITUNGAN JARAK TERPENDEK DALAM RUANG EIGEN

3-D Face Recognition System using Additional Feature Lines in Nearest Feature Line Method in Eigenspace Representation. In this paper, the authors propose a new method in 3-D face recognition system using additional feature lines in Nearest Feature Line method, called the Modified Nearest Feature Line method. The additional feature lines can be acquired by projecting each feature point to other feature lines in the same class without increasing the number of feature points. With these additional lines, the system will have the ability to capture more variations of face images, so it can increase the recognition rate of the system. The authors also propose KL-TSubspace1 and KL-TSubspace2 as methods in transforming the 3-D face images from its spatial domain to their eigenspace domain. The experiments use the 3-D human faces of Indonesian people in various expressions and positions. Then, the system is applied to recognize unknown face images with different viewpoints. Experimental results shown that the system using KL-TSubspace2 and Modified Nearest Feature Line method can have the highest recognition rate of 99.17%. Keywords: 3-D face recognition system, nearest feature line method (NFL), modified nearest feature line method (MNFL), Karhunen-Loeve transformation, eigenspace representation

Microstructural characterization of materials by neural network technique

Ultrasonic signals received by pulse echo technique from plane parallel Zircaloy 2 samples of fixed thickness and of three different microstructures, were subjected to signal analysis, as conventional parameters like velocity and attenuation could not reliably discriminate them. The signals, obtained from these samples, were first sampled and digitized. Modified Karhunen Loeve Transform was used to reduce their dimensionality. A multilayered feed forward Artificial Neural Network was trained using a few signals in their reduced domain from the three different microstructures. The rest of the signals from the three samples with different microstructures were classified satisfactorily using this network.

Lossy and lossless compression of MERIS hyperspectral images with exogenous quasi-optimal spectral transforms

Our research focuses on reducing complexity of hyperspectral image codecs based on transform and/or subband coding, so they can be on-board a satellite. It is well-known that the Karhunen Loeve transform (KLT) can be sub-optimal for non Gaussian data. However, it is generally recommended as the best calculable coding transform in practice. Now, for a compression scheme compatible with both the JPEG2000 Part2 standard and the CCSDS recommendations for onboard satellite image compression, the concept and computation of optimal spectral transforms (OST), at high bit-rates, were carried out, under low restrictive hypotheses. These linear transforms are optimal for reducing spectral redundancies of multi- or hyper-spectral images, when the spatial redundancies are reduced with a fixed 2-D discrete wavelet transform. The problem of OST is their heavy computational cost. In this paper we present the performances in coding of a quasi-optimal spectral transform, called exogenous OrthOST, obtained by learning an orthogonal OST on a sample of hyperspectral images from the spectrometer MERIS. Moreover, we compute an integer variant of OrthOST for lossless compression. The performances are compared to the ones of the KLT in both lossy and lossless compressions. We observe good performances of the exogenous OrthOST.