International Journal of Wavelets, Multiresolution and Information Processing

Hand and face gestures enable deaf people to communicate in their daily lives rather than speaking. This paper describes a hidden Markov model (HMM)-based framework for face sign recognition and detection. The observation vectors used to characterize the states of the HMM are obtained using the best tree local gradient pattern (LGP) encoded features. Each face gesture is modeled as a five-state HMM. The problem of facial expression classification is posed as a composite seven-classes multi-hypothesis Bayesian test. The likelihood ratio test showed that the overall recognition rate for the proposed model is higher than the HMM-local binary pattern descriptor by 6.4%. The overall recognition rate is enhanced by 8.6% using the discrete wavelet packet best tree decomposition filter as a pre-processing noise removal tool. In addition, the overall recognition rate ranges from 84.3%, for the seven classes Bayesian test, to 100%, for lower number of classes depending upon the type of the face gesture. The proposed face expression algorithm reduces significantly the computational complexity of previous HMM-based face expression recognition systems, and still preserve the recognition rate.

The field of medical image classification has been one of the most attention-gaining research areas in the recent times due to the increasing demand for an efficient tool that can help doctors in making quick and correct diagnoses. In this paper, a hybrid feature extraction technique is proposed, which is based on discrete wavelet transform (DWT), non-subsampled contourlet transform (NSCT) and isotropic gray level co-occurrence matrix (GLCM) for the categorization of grade II, III, and IV gliomas. The proposed method was applied on a dataset of 93 MRI brain images containing three glioma grades (23 grade II, 45 grade III, and 25 grade IV). The efficiency of proposed methodology is evaluated in terms of classification accuracy, sensitivity and specificity. The highest accuracy of $88.88\%$ for grade III, sensitivity of $95.65\%$ and specificity of $95.71\%$ were achieved in case of grade II.

The electrocardiogram (ECG) non-invasively monitors the electrical activities of the heart to diagnose the heart-related diseases. The baseline wandering noise affects the diagnosis of the heart diseases. In this paper, the baseline wandering noise removal is done using forward–backward Riemann Liouville (RL) fractional integral-based empirical wavelet transform (EWT) approach. In the designed methodology, firstly, the noisy ECG signal is decomposed into various modes from low to high frequencies. Then, the first mode is processed to remove the baseline wandering noise. The processed EWT mode is filtered by the fractional RL filter used in the forward direction and then in the backward direction for removing the baseline wandering noise from the ECG signal. After that, the processed and the unprocessed modes are used to reconstruct the denoised ECG signal. The clean ECG signal record is taken from MIT-BIH ECG-ID database, and the baseline wandering noise record is taken from the MIT-BIH noise stress test database. The performance of the proposed approach is validated in terms of the output signal-to-noise ratio (SNR${}_{\mathrm{\text{o}}}$). The comparative study has also been done between the proposed denoising approach and the existing state-of-the-art denoising algorithms. The experimental result proves the supremacy of our proposed denoising approach.

The continuous wavelet transform (CWT) associated with zero-order Mehler–Fock transform (MF-transform) is defined and discussed its some basic properties, Plancherel’s and Parseval’s relations, reconstruction formula for CWT are obtained. Further composition of CWT is investigated and then its Parseval’s and Plancherel’s relations are given. Moreover, time-invariant filter has been defined and proved convolution operator and wavelet transform are represented as time-invariant transform.

In this paper, we introduce and study woven approximate Schauder g-frames. We show that for any two approximate Schauder g-frames, each weaving is an approximate Schauder g-frame if and only if there is a uniform constant $C\ge 1$ such that every weaving is a C-approximate Schauder g-frame, and we obtain some perturbation results for approximate Schauder g-frames. Finally, some results have been found for weaving approximate Schauder g-frames.

In order to enhance efficiency of artificial intelligence (AI) tools such as classification or pattern recognition, it is important to have noise-free data to be processed with AI tools. Therefore, the study of algorithms used for reducing noise is also very significant. In thermal condition, Gaussian noise is important problem in analog circuit and image processing. Therefore, this paper focuses on the study of an algorithm for Gaussian noise reduction. In recent year, Bayesian with wavelet-based methods provides good efficiency in noise reduction and spends short time in processing. In Bayesian method, mixture density is more flexible than non-mixture density. Therefore, we proposed novel form of minimum mean square error (MMSE) estimation for mixture model, Pearson type VII and logistic densities, in Gaussian noise. The expectation-maximization (EM) algorithm is most deeply used for computing statistical parameters of mixture model. However, the EM estimator for the proposed method does not have the closed-form. Numerical methods are required to implement an EM algorithm. Therefore, we employ maximum a posteriori (MAP) estimation to compute local noisy variances with half-normal distribution prior for local noisy variances and Gaussian density for noisy wavelet coefficients. Here, the proposed method is expressed in closed-form. The denoising results present that our proposed algorithm outperforms the state-of-the-art method qualitatively and quantitatively.

In this paper, we give some new characterizations of g-frames, g-Bessel sequences and g-Riesz bases from their topological properties. By using the Gram matrix associated with the g-Bessel sequence, we present a sufficient and necessary condition under which the sequence is a g-Bessel sequence (or g-Riesz basis). Finally, we consider the excess of a g-frame and obtain some new results.

Images captured in foggy weather are severely degraded, which influences the tracking and recognition of objects present in those images. Therefore, restoring the true scene using a foggy image is important. In this paper, an effective fusion-based foggy image restoration technique by using dual tree complex wavelet transform (DT-CWT) has been proposed. Minimum color channel and the dark channel of a foggy image are constructed. Low and high pass components of both these channels are fused to obtain a transmission map. Dark channel is estimated by minimum preserving down sampling approach which improves the computational efficiency of the de-fogging process. Since DCP-based de-fogging techniques suffer from halo artifacts and darkness, proposed technique improves the overall contrast and the halo artifact regions in a time efficient way. To make the de-fogging results look uniformly bright, an adaptive post processing technique is applied on the de-fogged images. Comparative experiments with existing state-of-the-art algorithms show that de-fogging results of the proposed technique are better.

Phase-average technique based on wavelet multi-resolution analysis and continuous wavelet transform are used to reveal the phase-averaged features of square cylinder wake measured by high-speed PIV. The one-dimensional orthogonal wavelet analysis is first applied to decompose the measured velocity fields into large-, intermediate- and small-scale structures. Then the phase information referenced with large- and intermediate-scale flow structures are clearly identified based on Morlet wavelet transform. Finally, the data ensembles are phase-sorted to give phase-averaged representations of measured flow field. The instantaneous multi-scale structures suggest that large-scale vortices are weakened and begin to transfer into intermediate-vortices at the downstream of separation region. The intermediate-scale vortex observed at the upper boundary of shear layer is considered to be associated with the secondary vortex movement. The phase-averaged intermediate-scale structures tend to convey downstream along streamwise direction, with the rotation sense varying from the first half period to the last half period. The peaks of phase-averaged large-scale Reynolds stress tend to move back and forth in the near-wake region. These findings suggest that the proposed phase-average technique is effective in revealing multi-scale fluid dynamics of wake flow structures.

The theory of vector-valued frames (also called superframes) has important applications in signal multiplexing, and has interested many mathematicians in recent years. In this paper, we introduce the notion of weak Gabor duals of type II under the setting of subspaces $L^2(S,{ℂ}^L)$, where $S$ is a periodic subset of $ℝ$. Using the Zak transform matrix method, we characterize weak Gabor duals of type II and their uniqueness. An example is also presented to illustrate the generality of our results.

In this paper, we introduce and characterize controlled dual frames in Hilbert spaces. We also investigate the relation between bounds of controlled frames and their related frames. Then, we define the concept of approximate duality for controlled frames in Hilbert spaces. Next, we introduce multiplier operators of controlled frames in Hilbert spaces and investigate some of their properties. Finally, we show that the inverse of a controlled multiplier operator is also a controlled multiplier operator under some mild conditions.

In this paper, we address the problem of recovering signals from undersampled data where such signals are not sparse in an orthonormal basis, but in an overcomplete dictionary. We show that if the combined matrix obeys a certain restricted isometry property and if the signal is sufficiently sparse, the reconstruction that relies on ${\ell }_p$ minimization with $0<p<1$ is exact. In addition, under a mild assumption about the dictionary $D$, we use a similar method [H. Rauhut et al., Compressed sensing and redundant dictionaries, IEEE Trans. Inf. Theory 54(5) (2008) 2210–2219] to derive an estimation of the restricted isometry constant of the composed matrix $AD$. Finally, the performance of the ${\ell }_p$ minimization is testified by some numerical examples.