2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure

Single-shot fringe pattern phase retrieval using improved period-guided bidimensional empirical mode decomposition and Hilbert transform

Fringe pattern analysis is the central aspect of numerous optical measurement methods, e.g., interferometry, fringe projection, digital holography, quantitative phase microscopy. Experimental fringe patterns always contain significant features originating from fluctuating environment, optical system and illumination quality, and the sample itself that severely affect analysis outcome. Before the stage of phase retrieval (information decoding) interferogram needs proper filtering, which minimizes the impact of mentioned issues. In this paper we propose fully automatic and adaptive fringe pattern pre-processing technique - improved period guided bidimensional empirical mode decomposition algorithm (iPGBEMD). It is based on our previous work about PGBEMD which eliminated the mode-mixing phenomenon and made the empirical mode decomposition fully adaptive. In present work we overcame key problems of original PGBEMD – we have considerably increased algorithm’s application range and shortened computation time several-fold. We proposed three solutions to the problem of erroneous decomposition for very low fringe amplitude images, which limited original PGBEMD significantly and we have chosen the best one among them after comprehensive analysis. Several acceleration methods were also proposed and merged to ensure the best results. We combined our improved pre-processing algorithm with the Hilbert Spiral Transform to receive complete, consistent, and versatile fringe pattern analysis path. Quality and effectiveness evaluation, in comparison with selected reference methods, is provided using numerical simulations and experimental fringe data

BEMDEC: An Adaptive and Robust Methodology for Digital Image Feature Extraction

The intriguing study of feature extraction, and edge detection in particular, has, as a result of the increased use of imagery, drawn even more attention not just from the field of computer science but also from a variety of scientific fields. However, various challenges surrounding the formulation of feature extraction operator, particularly of edges, which is capable of satisfying the necessary properties of low probability of error (i.e., failure of marking true edges), accuracy, and consistent response to a single edge, continue to persist. Moreover, it should be pointed out that most of the work in the area of feature extraction has been focused on improving many of the existing approaches rather than devising or adopting new ones. In the image processing subfield, where the needs constantly change, we must equally change the way we think. In this digital world where the use of images, for variety of purposes, continues to increase, researchers, if they are serious about addressing the aforementioned limitations, must be able to think outside the box and step away from the usual in order to overcome these challenges. In this dissertation, we propose an adaptive and robust, yet simple, digital image features detection methodology using bidimensional empirical mode decomposition (BEMD), a sifting process that decomposes a signal into its two-dimensional (2D) bidimensional intrinsic mode functions (BIMFs). The method is further extended to detect corners and curves, and as such, dubbed as BEMDEC, indicating its ability to detect edges, corners and curves. In addition to the application of BEMD, a unique combination of a flexible envelope estimation algorithm, stopping criteria and boundary adjustment made the realization of this multi-feature detector possible. Further application of two morphological operators of binarization and thinning adds to the quality of the operator

ISAR Image formation with a combined Empirical Mode Decomposition and Time-Frequency Representation

International audienceIn this paper, a method for Inverse Synthetic Aperture Radar (ISAR) image formation based on the use of the Complex Empirical Mode Decomposition (CEMD) is proposed. The CEMD [1] which based on the Empirical Mode Decomposition (EMD) is used in conjunction with a Time-Frequency Representation (TFR) to estimate a 3-D time-range-Doppler Cubic image, which we can use to effectively extract a sequence of ISAR 2-D range-Doppler images. The potential of the proposed method to construct ISAR image is illustrated by simulations results performed on synthetic data and compared to 2-D Fourier Transform and TFR methods. The simulation results indicate that this method can provide ISAR images with a good resolution. These results demonstrate the potential application of the proposed method for ISAR image formation

BEMD Based Cross Bilateral Filtering Technique for Speckle Reduction in Ultrasound Images

In this paper, Bidimensional Empirical Mode Decomposition (BEMD) based Cross Bilateral Filter (CBF) technique for speckle reduction in ultra- sound images has been proposed. The reference image is obtained by denoising the noisy image using pixel- wise Wiener filtering. Then, both the noisy image and the reference image are decomposed into a set of In- trinsic Mode Functions (IMFs) and the residue im- age using BEMD technique. CBF is applied between noisy image IMFs and the corresponding reference im- age IMFs. The image is reconstructed back with these modified IMFs and the residue. The proposed method exploits the edge information in the reference image for improving the quality of the denoised image. The per- formance of the proposed method has been tested for real ultrasound images and simulated images having noise of different variance. The experimental results show that the proposed algorithm performs better than other state-of-art methods in terms of Edge Keeping Index (EKI), Correlation Coefficient (CC), Figure of Merit (FOM), Structural Similarity (SSIM), Peak Sig- nal to Noise Ratio (PSNR) and Signal to Noise Ratio (SNR) for synthetic images. The algorithm gives bet- ter performance for real ultrasound images in terms of Mean to Variance Ratio (MVR) and Equivalent Num- ber of Looks (ENL)