Ground roll extraction using the Karhunen-Loeve transform in the time-frequency domain

Ground roll suppression is critical for seismic reflection data processing. Many standard methods, i.e., FK filtering, fail when spatially aliased surface wave interference is present in the data. Spatial aliasing is a common problem; receiver spacing is often not dense enough to extract wavenumbers of low-velocity surface waves. It has long been known that the Karhunen-Loeve transform can be used to suppress aliased ground roll. However, the ground roll should be flattened before suppression, which is challenging due to the dispersion of surface wave velocities. I propose to solve this problem via the time-frequency domain. I apply the S-transform, which was previously shown to perform well in the multichannel analysis of surface waves. A simple complex-valued constant phase shift is a suitable model of surface wave propagation in common-frequency S-transform gathers. Therefore, it is easy to flatten the corresponding S-transform narrow-band frequency surface wave packet and extract it from the data by principal component analysis of the corresponding complex-valued data-covariance matrix. As the result, the proposed S-transform Karhunen-Loeve (SKL) method filters the aliased ground roll without damaging the reflection amplitudes. The advantages of SKL filtering have been confirmed by synthetic- and field-data processing.

Automatic Segmentation and Measurement of Infantile Hemangioma

Infantile hemangiomas (IHs) are a type of vascular tumors that affect around 10% of newborns. The measurement of the lesion size and the assessment of the evolution is done manually by the physician. This paper presents an algorithm for the automatic computation of the IH lesion surface. The image scale is computed by using the Hough transform and the total variation. As pre-processing, a geometric correction step is included, which ensures that the lesions are viewed as perpendicular to the camera. The image segmentation is based on K-means clustering applied on a five-plane image; the five planes being selected from seven planes with the use of the Karhunen-Loeve transform. Two of the seven planes are 2D total variation filters, based on symmetrical kernels, designed to highlight the IH specific texture. The segmentation performance was assessed on 30 images, and a mean border error of 9.31% was obtained.

Complexity Estimation of Cubical Tensor Represented through 3D Frequency-Ordered Hierarchical KLT

In this work is introduced one new hierarchical decomposition for cubical tensor of size 2n, based on the well-known orthogonal transforms Principal Component Analysis and Karhunen–Loeve Transform. The decomposition is called 3D Frequency-Ordered Hierarchical KLT (3D-FOHKLT). It is separable, and its calculation is based on the one-dimensional Frequency-Ordered Hierarchical KLT (1D-FOHKLT) applied on a sequence of matrices. The transform matrix is the product of n sparse matrices, symmetrical at the point of their main diagonal. In particular, for the case in which the angles which define the transform coefficients for the couples of matrices in each hierarchical level of 1D-FOHKLT are equal to π/4, the transform coincides with this of the frequency-ordered 1D Walsh–Hadamard. Compared to the hierarchical decompositions of Tucker (H-Tucker) and the Tensor-Train (TT), the offered approach does not ensure full decorrelation between its components, but is close to the maximum. On the other hand, the evaluation of the computational complexity (CC) of the new decomposition proves that it is lower than that of the above-mentioned similar approaches. In correspondence with the comparison results for H-Tucker and TT, the CC decreases fast together with the increase of the hierarchical levels’ number, n. An additional advantage of 3D-FOHKLT is that it is based on the use of operations of low complexity, while the similar famous decompositions need large numbers of iterations to achieve the coveted accuracy.

Fragile Watermarking of 3D Models in a Transformed Domain

This paper presents an algorithm aimed at the integrity protection of 3D models represented as a set of vertices and polygons. The proposed method defines a procedure to perform a fragile watermarking of the vertices’ data, namely 3D coordinates and polygons, introducing a very small error in the vertices’ coordinates. The watermark bit string is embedded into a secret vector space defined by the Karhunen–Loève transform derived from a key image. Experimental results show the good performance of the method and its security.

Performance analysis of the Karhunen–Loève Transform for artificial and astrophysical transmissions: denoizing and detection

ABSTRACT In this work, we propose a new method of computing the Karhunen–Loève Transform (KLT) applied to complex voltage data for the detection and noise level reduction in astronomical signals. We compared this method with the standard KLT techniques based on the Toeplitz correlation matrix and we conducted a performance analysis for the detection and extraction of astrophysical and artificial signals via Monte Carlo (MC) simulations. We applied our novel method to a real data study-case: the Voyager 1 telemetry signal. We evaluated the KLT performance in an astrophysical context: our technique provides a remarkable improvement in computation time and MC simulations show significant reconstruction results for signal-to-noise ratio (SNR) down to −10 dB and comparable results with standard signal detection techniques. The application to artificial signals, such as the Voyager 1 data, shows a notable gain in SNR after the KLT.

Chimera: A New Efficient Transform for High Quality Lossy Image Compression

A novel scheme is presented for image compression using a compatible form called Chimera. This form represents a new transformation for the image pixels. The compression methods generally look for image division to obtain small parts of an image called blocks. These blocks contain limited predicted patterns such as flat area, simple slope, and single edge inside images. The block content of these images represent a special form of data which be reformed using simple masks to obtain a compressed representation. The compression representation is different according to the type of transform function which represents the preprocessing operation prior the coding step. The cost of any image transformation is represented by two main parameters which are the size of compressed block and the error in reconstructed block. Our proposed Chimera Transform (CT) shows a robustness against other transform such as Discrete Cosine Transform (DCT), Wavelet Transform (WT) and Karhunen-Loeve Transform (KLT). The suggested approach is designed to compress a specific data type which are the images, and this represents the first powerful characteristic of this transform. Additionally, the reconstructed image using Chimera transform has a small size with low error which could be considered as the second characteristic of the suggested approach. Our results show a Peak Signal to Noise Ratio (PSNR) enhancement of 2.0272 for DCT, 1.179 for WT and 4.301 for KLT. In addition, a Structural Similarity Index Measure (SSIM) enhancement of 0.1108 for DCT, 0.051 for WT and 0.175 for KLT.

Saak Transform-Based Machine Learning for Light-Sheet Imaging of Cardiac Trabeculation

Recent advances in light-sheet fluorescence microscopy (LSFM) enable 3-dimensional (3-D) imaging of cardiac architecture and mechanics in toto. However, segmentation of the cardiac trabecular network to quantify cardiac injury remains a challenge. We hereby employed “subspace approximation with augmented kernels (Saak) transform” for accurate and efficient quantification of the light-sheet image stacks following chemotherapy-treatment. We established a machine learning framework with augmented kernels based on the Karhunen-Loeve Transform (KLT) to preserve linearity and reversibility of rectification. The Saak transform-based machine learning enhances computational efficiency and obviates iterative optimization of cost function needed for neural networks, minimizing the number of training data sets to three 2-D slices for segmentation in our scenario. The integration of forward and inverse Saak transforms serves as a light-weight module to filter adversarial perturbations and reconstruct estimated images, salvaging robustness of existing classification methods. The accuracy and robustness of the Saak transform are evident following the tests of dice similarity coefficients and various adversary perturbation algorithms, respectively. The addition of edge detection further allows for quantifying the surface area to volume ratio (SVR) of the myocardium in response to chemotherapy-induced cardiac remodeling. The combination of Saak transform, random forest, and edge detection augments segmentation efficiency by 20-fold as compared to manual processing; thus, establishing a robust framework for post light-sheet imaging processing, creating a data-driven machine learning for 3-D quantification of cardiac ultra-structure.