Complex Wavelet Filters Research Articles

Complex wavelet filter improves FLIM phasors for photon starved imaging experiments.

Fluorescence lifetime imaging microscopy (FLIM) with phasor analysis provides easy visualization and analysis of fluorophores' lifetimes which is valuable for multiple applications including metabolic imaging, STED imaging, FRET imaging and functional imaging. However, FLIM imaging typically suffers from low photon budgets, leading to unfavorable signal to noise ratios which in many cases prevent extraction of information from the data. Traditionally, median filters are applied in phasor analysis to tackle this problem. This unfortunately degrades high spatial frequency FLIM information in the phasor analysis. These high spatial frequency components are typically edges of features and puncta, which applies to membranes, mitochondria, granules and small organelles in a biological sample. To tackle this problem, we propose a filtering strategy with complex wavelet filtering and Anscombe transform for FLIM phasor analysis. This filtering strategy preserves fine structures and reports accurate lifetimes in photon starved FLIM imaging. Moreover, this filter outperforms median filters and makes FLIM imaging with lower laser power and faster imaging possible.

Rotational Wavelet Filters for Analysis of Brain MRI in Detection of Alzheimer’s Disease

In this paper, a method is suggested for multi directional analysis of Magnetic Resonance Image (MRI) scans for detection of Alzheimer’s disease (AD). This is a novel technique which utilizes, two-dimensional (2-D) rotated complex wavelet filters (RCWF) for feature identification. DTCWT identifies the features in 6 directions (±150±450, ±750) while RCWT identifies the features in different 6 directions (-300,0, +300, +600, +900, +1200), which enhances the directional selectivity of the transform coefficients and results in well description of corresponding textures. Dual-tree rotated complex wavelet transform (DT- RCWF) and dual-tree complex wavelet transform (DT- CWT) are applied to the sample images at a time thus the transform coefficients in twelve different directions is obtained simultaneously. The obtained transform coefficients are used for calculation of various texture features such as energy, entropy and standard deviation. The obtained parameters form the feature vectors which are given as input to the classifiers to get the input classified as Normal control or AD sufferer. This proposed algorithm produces results which are superior in terms of accuracy, feature extraction rate, sensitivity, specificity, precision and recall necessary to realize the efficiency of diagnosis of Alzheimer’s Disease as compared to other existing methods.

Bearing Fault Signal Analysis Based on an Adaptive Multiscale Combined Morphological Filter

Bearing fault signal analysis is an important means of bearing fault diagnosis. To effectively eliminate noise in a fault signal, an adaptive multiscale combined morphological filter is proposed based on the theory of mathematical morphology. Both simulation and experimental results show that the adaptive multiscale combined morphological filter can remove noise more thoroughly and retain details of the fault signal better than the dual-tree complex wavelet filter, traditional morphological filter, adaptive singular value decomposition method (ASVD), and improved switching Kalman filter (ISKF). The adaptive multiscale combined morphological filter considers both positive and negative impulses in the signal; therefore, it has strong adaptability to complex noise in the environment, making it an effective new method for bearing fault diagnosis.

SAR Automatic Target Recognition Using a Roto-Translational Invariant Wavelet-Scattering Convolution Network

The algorithm of synthetic aperture radar (SAR) for automatic target recognition consists of two stages: feature extraction and classification. The quality of extracted features has significant impacts on the final classification performance. This paper presents a SAR automatic target classification method based on the wavelet-scattering convolution network. By introducing a deep scattering convolution network with complex wavelet filters over spatial and angular variables, robust feature representations can be extracted across various scales and angles without training data. Conventional dimension reduction and a support vector machine classifier are followed to complete the classification task. The proposed method is then tested on the moving and stationary target acquisition and recognition (MSTAR) benchmark data set and achieves an average accuracy of 97.63% on the classification of ten-class targets without data augmentation.

Balancing accuracy, delay and battery autonomy for pervasive seizure detection.

A promising alternative for treating absence seizures has emerged through closed-loop neurostimulation, which utilizes a wearable or implantable device to detect and subsequently suppress epileptic seizures. Such devices should detect seizures fast and with high accuracy, while respecting the strict energy budget on which they operate. Previous work has overlooked one or more of these requirements, resulting in solutions which are not suitable for continuous closed-loop stimulation. In this paper, we perform an in-depth design space exploration of a novel seizure-detection algorithm, which uses a complex Morlet wavelet filter and a static thresholding mechanism to detect absence seizures. We consider both the accuracy and speed of our detection algorithm, as well as various trade-offs with device autonomy when executed on a low-power processor. For example, we demonstrate that a minimal decrease in average detection rate of only 1.83% (from 92.72% to 90.89%) allows for a substantial increase in device autonomy (of 3.7x) while also facilitating faster detection (from 710 ms to 540 ms).

Structure and realization of pole-shared switched-current complex wavelet filter

A pole-shared switched-current complex wavelet filter structure with follow-the-leader feedback configuration is proposed for synthesizing the real and imaginary approximation functions with the same poles. The double-sampling fully-balanced SI bilinear integrator and current mirror are employed as the building cells. By sharing the implementation circuit for approximation poles of the real and the imaginary part, the proposed structure only has the same circuit complexity as that of real-valued wavelet filter, which is very suitable for small-size and low-power application. The complex Morlet wavelet is selected as an example to elaborate the design procedure. Simulation results confirm that the presented complex wavelet filter structure can generate the real and imaginary coefficients of complex wavelet transform accurately with simple synthesis method and explicit design formulas.

Speech frame recognition based on less shift sensitive wavelet filter banks

The wavelet transform possesses multi-resolution property and high localization performance; hence, it can be optimized for speech recognition. In our previous work, we show that redundant wavelet filter bank parameters work better in speech recognition task, because they are much less shift sensitive than those of critically sampled discrete wavelet transform (DWT). In this paper, three types of wavelet representations are introduced, including features based on dual-tree complex wavelet transform (DT-CWT), perceptual dual-tree complex wavelet transform, and four-channel double-density discrete wavelet transform (FCDDDWT). Then, appropriate filter values for DT-CWT and FCDDDWT are proposed. The performances of the proposed wavelet representations are compared in a phoneme recognition task using special form of the time-delay neural networks. Performance evaluations confirm that dual-tree complex wavelet filter banks outperform conventional DWT in speech recognition systems. The proposed perceptual dual-tree complex wavelet filter bank results in up to approximately 9.82 % recognition rate increase, compared to the critically sampled two-channel wavelet filter bank.

Automatic logo based document image retrieval

Recently, there is need for the automatic logo detection and document image retrieval because of increasing requirements of intelligent document images. In this work, we have developed an automatic logo based document image retrieval system in which we first proposed an automatic logo detection and extraction from the document images using discrete wavelet transform (DWT). Then, we have proposed an approach to retrieve document images based on the logo using combined rotated complex wavelet filters (RCWF) and dual tree complex wavelet transform (DT-CWT). Since these combined features give information in twelve different directions. Our approach is segmentation free. Finally, we evaluate the effectiveness of our approach using large database collections of real-world complex documents.

Interactive Semantic Image Retrieval

The big challenge in current content-based image retrieval systems is to reduce the semantic gap between the low level-features and high-level concepts. In this paper, we have proposed a novel framework for efficient image retrieval to improve the retrieval results significantly as a means to addressing this problem. In our proposed method, we first extracted a strong set of image features by using the dual-tree rotated complex wavelet filters (DT-RCWF) and dual tree-complex wavelet transform (DT-CWT) jointly, which obtains features in 12 different directions. Second, we presented a relevance feedback (RF) framework for efficient image retrieval by employing a support vector machine (SVM), which learns the semantic relationship among images using the knowledge, based on the user interaction. Extensive experiments show that there is a significant improvement in retrieval performance with the proposed method using SVMRF compared with the retrieval performance without RF. The proposed method improves retrieval performance from 78.5% to 92.29% on the texture database in terms of retrieval accuracy and from 57.20% to 94.2% on the Corel image database, in terms of precision in a much lower number of iterations.

A joint sparse wavelet coefficient extraction and adaptive noise reduction method in recovery of weak bearing fault features from a multi-component signal mixture

Rolling element bearings are widely used to support rotating components of a machine. Due to close space locations of components in the machine, a vibration signal caused by bearing localized defects is easily overwhelmed by other strong vibration signals. Extracting the bearing fault signal from a multi-component signal mixture is thus significant to detect early bearing fault features and prevent machine breakdown. In this paper, a bearing fault diagnosis method, named cyclic spike detection method, is proposed to extract the weak bearing fault features from a multi-component signal mixture. Firstly, the optimal center frequency and bandwidth of a complex Morlet wavelet filter are determined by a simplex-simulated annealing algorithm along with a maximum sparsity objective function. The filtered signal is then obtained by applying the optimal wavelet filter to the multi-component signal mixture. After that, a new adaptive local maximum selection method is proposed to make the filtered signal succinct. Only a few spikes are retained to reveal potential cyclic intervals caused by bearing localized defects. Two multi-component signal mixtures, including a simulated signal and a real vibration signal collected from an industrial machine, are used to validate the effectiveness of the proposed cyclic spike detection method. The results demonstrate that the proposed method can extract the weak bearing fault features from other strong masking vibration signals and noise.

Performance of an Improved MC-CDMA System Based on DT-OCWDM and Quasi-Orthogonal Matrix

In this paper, we propose a new improved MC-CDMA system which combines spreading codes from Quasi-Orthogonal Matrix with Orthogonal Complex Wavelet Division Multiplexing (OCWDM). The system is implemented by complex wavelet filters which are able to lower computational complexity and increase flexibility. Novel spreading codes from Quasi-Orthogonal Matrix can be expanded randomly. It can increase user number hugely in system. Improved MC-CDMA named OCWDM-CDMA has much higher frequency spectrum efficiency and high data rate than conventional MC-CDMA. The system also has better BER performance in Gaussian channel than conventional system for much more users.

The Application of Complex Wavelet Transform to Spectral Signals Background Deduction

The accuracy of spectrograms may be affected by baseline excursion or drift when infrared spectrometers are used in the analyses of gases. Background deduction or baseline correction is one of the effective pretreatment methods that can improve measurement accuracy. This paper presents a novel methodology based on complex wavelet transform algorithm to perform background deduction. The complex wavelet transform methodology establishes a complex wavelet filter to decompose the spectral signals first, and set the decomposition coefficients in the high-frequency section to zero, and then reconstruct the background signals; finally, the background deduction can be realized by deducting the background signals. In this study, the complex wavelet established by Daubechies was selected to demonstrate background deduction aiming at simulative spectral signals with different backgrounds and the real spectral signal of SF6 decomposition gases. Compared with the results done by the real wavelet transform in the same conditions, the results indicate that complex wavelet transform methodology can perform background deduction more efficiently than real wavelet transform methodology, thus improving the effectiveness and precision of spectrogram measurements greatly, which is useful for SF6 gas decomposition compositions analysis

Rotation-Invariant Texture Image Retrieval Using Rotated Complex Wavelet Filters

This paper proposes a novel approach for rotation-invariant texture image retrieval by using set of dual-tree rotated complex wavelet filter (DT-RCWF) and DT complex wavelet transform (DT-CWT) jointly, which obtains texture features in 12 different directions. Two-dimensional RCWFs are nonseparable and oriented, which improves characterization of oriented textures. Robust and efficient isotropic rotationally invariant features are extracted from DT-RCWF and DT-CWT decomposed subbands. This paper demonstrates the effectiveness of this new set of features on four different sets of rotated and nonrotated databases. Experimental results indicate that the proposed method improves retrieval accuracy from 83.17% to 93.71% on a small size (208 images) nonrotated database D1, from 82.71% to 90.86% on a small size (208 images) rotated database D2, from 72.18% to 76.09% on a medium-size (640 images) rotated database D3, and from 64.17% to 78.93% on a large size (1856 images) rotated database D4, compared with the discrete wavelet transform-based approach. New method also retains comparable levels of computational complexity.

Texture Image Retrieval Using New Rotated Complex Wavelet Filters

A new set of two-dimensional (2-D) rotated complex wavelet filters (RCWFs) are designed with complex wavelet filter coefficients, which gives texture information strongly oriented in six different directions (45 degrees apart from complex wavelet transform). The 2-D RCWFs are nonseparable and oriented, which improves characterization of oriented textures. Most texture image retrieval systems are still incapable of providing retrieval result with high retrieval accuracy and less computational complexity. To address this problem, we propose a novel approach for texture image retrieval by using a set of dual-tree rotated complex wavelet filter (DT-RCWF) and dual-tree-complex wavelet transform (DT-CWT) jointly, which obtains texture features in 12 different directions. The information provided by DT-RCWF complements the information generated by DT-CWT. Features are obtained by computing the energy and standard deviation on each subband of the decomposed image. To check the retrieval performance, texture database D1 of 1856 textures from Brodatz album and database D2 of 640 texture images from VisTex image database is created. Experimental results indicates that the proposed method improves retrieval rate from 69.61% to 77.75% on database D1, and from 64.83% to 82.81% on database D2, in comparing with traditional discrete wavelet transform based approach. The proposed method also retains comparable levels of computational complexity.

Hilbert transform assisted complex wavelet transform for neuroelectric signal analysis

In this work, we present a new approach for shift invariant complex wavelet analysis of neuroelectric signals. A key idea is to preprocess the signal with the Hilbert transformer to yield an analytic signal, which is then wavelet transformed using the linear phase complex scaling and wavelet filters. In different scales, the total energy of the wavelet transform coefficients is shift invariant. The decimated analytic wavelet coefficients suffer no aliasing effects, which are predominant in conventional wavelet analysis. We show the usefulness of the present method in multi-scale analysis of the neuroelectric signal waveforms.

'Analytic' wavelet thresholding

SUMMARY We introduce so-called analytic stationary wavelet transform thresholding where, using the discrete Hilbert transform, we create a complex-valued 'analytic' vector from which an amplitude vector is defined. Thresholding of a real-valued wavelet coefficient at some transform level is carried out according to the corresponding value in this amplitude vector; relevant statistical results follow from properties of the discrete Hilbert transform. Analytic stationary wavelet transform thresholding is found to produce consistently a reduced mean squared error compared to using standard stationary wavelet transform, or 'cycle spinning', thresholding. For signals with extensive oscillations at some transform levels, this improvement is very marked. Furthermore we show that our thresholding test is invariant to phase shifts in the data, whereas, if complex wavelet filters are being used, the filters must be analytic or anti-analytic at each level of the wavelet transform.