A New Adaptive TV-Based BM3D Algorithm for Image Denoising

The shrinkage function has an important effect on the image denoising results. An adaptive shrinkage function is developed in this paper to shrink the small coefficients properly for image denoising based on neighborhood characteristics. The shrinkage function is determined by the number of large coefficients near the current signal coefficients. In this way, different shrinkage functions can be adaptively used to deal with different coefficients in the process of image denoising, instead of using fixed shrinkage functions. Experimental results show that the SNR of the image processed by the adaptive shrink function algorithm is better than that processed by the soft threshold, hard threshold, and neighborhood shrink algorithm. Moreover, compared with the traditional soft threshold, hard threshold and neighborhood shrink algorithm, the PSNR of the algorithm using adaptive shrink function increases by 3.68dB, 2.28dB and 0.61dB, respectively. In addition, the proposed new algorithms, soft threshold and hard threshold, are combined with empirical Wiener filtering and shift invariant (TI) scheme to compare their image noise reduction effects. The results show that the PSNR can be improved significantly by using the adaptive shrink function algorithm combined with empirical Wiener filtering and shift invariant (TI) scheme.

Compressed sensing aims to recover the sparse signal from small linear random combination. The recovery process of the sparse signal through an underdetermined system is the most challenging part of the compressed sensing area. Recently, there are many algorithms have been developed for the recovery process to solve the optimization problem such as hard thresholding, greedy and convex optimization algorithms. In this paper, modifications of hard thresholding algorithms are proposed. An iterative algorithm is introduced which is called Forward and Backward Hard Thresholding algorithm (FBHT). It depends on two stages. One expands the support size and the other removes some elements from it with the guarantee of expanding the support size after each iteration. The forward and the backward steps are continued until reaching of the minimum value of residual by using a certain threshold. Many simulation programs are executed to compare the performance of the proposed FBHT algorithm with the related previous ones. The FBHT algorithm outperforms the previous ones in chosen performance metrics which are the mean square error and the signal to error ratio. Furthermore, the impact of some related parameters of the proposed FBHT algorithm and the impact of the sparsity level is discussed.

Wavelet de-noising method is often used in the processing of magnetotelluric (MT) signal, and the wavelet hard and soft threshold de-noising method are the most popular although there is much room for improvement in the threshold function selection and threshold determination. A new adaptive wavelet threshold de-noising method was proposed by selecting a new threshold function and presenting an adaptive method for obtaining optimal threshold based on the multi-resolution Stein unbiased risk estimation. New threshold function and an adaptive method to determine threshold were discussed, and the principle and implementation of the algorithm were given. The simulated signal and the measured MT data contaminated by impulse interference were analyzed, and the obtained results were compared with those of the conventional wavelet hard and soft threshold de-noising methods. The results show that the proposed method overcomes the defects of the traditional wavelet soft and hard threshold due to a new threshold function, and a new method to determine the threshold of each layer is applied and provides an adaptive method for filtering MT data in the wavelet domain that requires a minimum of human intervention. The presented de-noising method is very suitable for suppressing the impulse interference for MT data and can get higher signal-to-noise ratio than the traditional wavelet threshold de-noising methods. After de-noising, the accurate data is loaded for further impedance estimation and geological interpretation.

Acoustic emission (AE) detection, as a non-electrical detection method, is very suitable for effective fault detection of power equipment with a strong electromagnetic field. However, the AE signal collected at industrial sites often contains a lot of interference noise, affecting the analysis and prediction of faults. In this study, a wavelet denoising method based on a new threshold function is proposed, to achieve a noise reduction in the low signal-to-noise ratio (SNR) signals. Simulation experiment results show that the proposed threshold function not only overcomes the shortcomings of the discontinuous hard threshold function, but also solves the constant deviation of the soft threshold function. What’s more, the proposed function achieves a good adaptability. When SNR = 10 dB: The SNR of the new threshold is 20.6622, and the RMSE is 0.0026. The SNR of the hard threshold is 20.2246 and the RMSE is 0.0027, compared with the traditional hard threshold method, the SNR of the new threshold is increased by 2.16% and the root mean square error (RMSE) is reduced by 3.7%; the SNR of the soft threshold is 15.5656, and the RMSE is 0.0047, compared with the traditional soft threshold method, the new threshold has a 32.74% increase in SNR and a 40.43% reduction in RMSE. When SNR = -10 dB: The SNR of the new threshold is 4.2602, and the RMSE is 0.0172. The SNR of the hard threshold is 3.8558 and the RMSE is 0.0182, compared with the traditional hard threshold method, the SNR of the new threshold is increased by 10.49% and the RMSE is reduced by 5.49%; the SNR of the soft threshold is 2.1625, and the RMSE is 0.0212, compared with the soft threshold method, SNR is improved by 97% and RMSE is reduced by 18.87%. Performance analyses have proved that the improved wavelet denoising method can obtain a good noise reduction effect. It is very helpful for AE signal analysis with the generally low SNR, which can improve the accuracy of failure identification in subsequent acts.

On the basis of wavelet theory, a novel Adaptive wavelet thresholding method (AWT) is proposed for the ECG signal enhancement. The best base wavelet for ECG signal filtering can be automatically obtained through the cross correlation coefficient and the energy to entropy ratio. The variable universal threshold (VarUniversal) is applied to different decomposition level so as to suppress diverse noise. To achieve a smooth cut-off transition, an identical correlation shrinkage function (IcoShrinkage) is also adopted in the AWT according to its correlation coefficients with the hard thresholding and the soft thresholding. The performance of AWT is compared with four threshold approaches and six shrinkage functions, respectively, on the basis of 150 practical ECG signals of 30 subjects. The filtering results reveal that the AWT can adaptively choose an optimal base wavelet for a specific ECG signal. With the VarUniversal threshold and IcoShrinkage, the AWT obtains the better filtering results than the other compared methods.

Electrocardiogram (ECG) signal is the most direct means of detecting human health condition. In the process of acquisition, ECG will be contaminated by all kinds of noises and interferences, while the effects of traditional wavelet denoising algorithms are not very satisfying. This paper presented a novel thresholding method based on Discrete Wavelet Transform (DWT). Compared with the traditional hard thresholding and soft thresholding, it can effectively suppress all kinds of high-frequency and lowfrequency noises. To a certain extent, the novel thresholding method protects the characteristics and amplitude of ECG signal perfectly. Finally, MIT-BIH arrhythmia database was used to verify this novel thresholding method; the experimental results showed that the performance of the proposed algorithm is better than the traditional wavelet thresholding algorithms. This proposed new thresholding algorithm can maintain the geometrical characteristics of ECG signal much better, and it also has higher Signal Noise Ratio (SNR).

Partial Discharge (PD) signal measurement is very significant tool in analyzing condition of the electrical insulation. The PD information is lost in the presence of various noises. The wavelet transform (WT) based denoising provides a better platform for pre and post processing of PD signal. The wavelet adaptive Thresholding de-noising techniques are well suited for reducing the noise. This paper adopts the various adaptive thresholding techniques such as VisuShrink, SureShrink, combination of the two called Heursure, minimax thresholding and BayesShrink, which are broadly classified as Global and Local thresholding methods. The algorithm presents the comparative analysis for the selection of optimal mother wavelet. Once the optimal mother wavelet is chosen, selection of the best thresholding rule is identified by comparing the values of signal to noise ratio (SNR), mean square error (MSE) and Peak Signal to Noise ratio (PSNR) of all the techniques. The algorithm also presents the comparison between Hard and Soft thresholding. It is shown that the soft thresholding is best suited to remove the noise compared to hard thresholding. The simulated Damped Exponential Pulse (DEP) and Damped Oscillatory Pulse (DOP) has been used. Three sets of PD data are considered to check the performance of the algorithm.

Scanning acoustic microscopy (SAM) is a label-free imaging technique used in biomedical imaging, non-destructive testing, and material research to visualize surface and sub-surface structures. In ultrasonic imaging, noises in images can reduce contrast, edge and texture details, and resolution, negatively impacting post-processing algorithms. To reduce the noises in the scanned image, we have employed a 4D block-matching (BM4D) filter that can be used to denoise acoustic volumetric signals. BM4D filter utilizes the transform domain filtering technique with hard thresholding and Wiener filtering stages. The proposed algorithm produces the most suitable denoised output compared to other conventional filtering methods (Gaussian filter, median filter, and Wiener filter) when applied to noisy images. The output from the BM4D-filtered images was compared to the noise level with different conventional filters. Filtered images were qualitatively analyzed using metrics such as structural similarity index matrix (SSIM) and peak signal-to-noise ratio (PSNR). The combined qualitative and quantitative analysis demonstrates that the BM4D technique is the most suitable method for denoising acoustic imaging from the SAM. The proposed block matching filter opens a new avenue in the field of acoustic or photoacoustic image denoising, particularly in scenarios with poor signal-to-noise ratios.

Compressed sensing (CS) is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper, we apply the iterative hard thresholding (IHT) algorithm for compressed sensing on the speech signal. The interested speech signal is transformed to the frequency domain using Discrete Fourier Transform (DCT) and then compressed sensing is applied to that signal. The compressed signal can be reconstructed using the recently introduced Iterative Hard Thresholding (IHT) algorithm and also by the tradditional \( \ell_{1} \) minimization (basic pursuit) for comparison. It is shown that the compressed sensing can provide better root mean square error (RMSE) than the tradition DCT compression method, given the same compression ratio.

Step detection for smartphones plays an important role in the pedestrian dead reckoning (PDR) for indoor positioning. Aiming at the problem of low step detection accuracy of smartphones in complex unconstrained states in PDR, smartphone-based unconstrained step detection method fusing a variable sliding window and an adaptive threshold is proposed. In this method, the dynamic updating algorithm of a peak threshold is developed, and the minimum peak value filtered after a sliding window filter is used as the adaptive peak threshold, which solves the problem that the peak threshold of different motion states is difficult to update adaptively. Then, a variable sliding window collaborative time threshold method is proposed, which solves the problem that the adjacent windows cannot be contacted, and the initial peak and the end peak are difficult to accurately identify. To evaluate the performance of the proposed unconstrained step detection algorithm, 50 experiments in constrained and unconstrained states are conducted by 25 volunteers holding 21 different types of smartphones. Experimental results show: The average step counting accuracy of the proposed unconstrained step detection algorithm is over 98%. Compared with the open source program Stepcount, the average step counting accuracy of the proposed algorithm is improved by 10.0%. The smartphone-based unconstrained step detection fusing a variable sliding window and an adaptive threshold has a strong ability to adapt to complex unconstrained states, and the average step counting accuracy rate is only 0.6% lower than that of constrained states. This algorithm has a wide audience and is friendly for different genders and smartphones with different prices.

Compressive radar imaging has attracted considerable attention because it substantially reduces imaging time through directly compressive sampling. However, a problem that must be addressed for compressive radar imaging systems is the high computational complexity of reconstruction of sparse signals. In this paper, a novel algorithm, called two-dimensional (2D) normalized iterative hard thresholding (NIHT) or 2D-NIHT algorithm, is proposed to directly reconstruct radar images in the matrix domain. The reconstruction performance of 2D-NIHT algorithm was validated by an experiment on recovering a synthetic 2D sparse signal, and the superiority of the 2D-NIHT algorithm to the NIHT algorithm was demonstrated by a comprehensive comparison of its reconstruction performance. Moreover, to be used in compressive radar imaging systems, a 2D sampling model was also proposed to compress the range and azimuth data simultaneously. The practical application of the 2D-NIHT algorithm in radar systems was validated by recovering two radar scenes with noise at different signal-to-noise ratios, and the results showed that the 2D-NIHT algorithm could reconstruct radar scenes with a high probability of exact recovery in the matrix domain. In addition, the reconstruction performance of the 2D-NIHT algorithm was compared with four existing efficient reconstruction algorithms using the two radar scenes, and the results illustrated that, compared to the other algorithms, the 2D-NIHT algorithm could dramatically reduce the computational complexity in signal reconstruction and successfully reconstruct 2D sparse images with a high probability of exact recovery.

In this letter, the authors propose block normalised iterative hard thresholding (BNIHT) algorithm for the recovery of block sparse signal, in which the non-zero elements are presented in clusters. Based on block restricted isometry property, the sufficient conditions to guarantee the convergence of BNIHT are derived. In addition, the number of required iterations is obtained. The simulation experiment shows that BNIHT algorithm is superior to the block IHT (BIHT) algorithm when the step size satisfies μ < 1 .

There has been a growing interest in compressed wideband spectrum sensing. One significant challenge in this field is how to effectively overcome the sparsity dependence. To solve this, two adaptive sparsity methods based on one-bit compressed sensing are explored for wideband spectrum sensing. One method (ASBIHT) is proposed by introducing adaptive sparsity into the binary iterative hard threshold method (BIHT). Using the magnitude of energy, it can accurately reconstruct the signals with unknown sparsity by learning the signal and noise. The other method is constructed by combining the binary iterative hard threshold algorithm with the pinball loss function (PIHT), and adaptive sparsity (ASPIHT). Utilizing the fixed step, the hard threshold parameter is adjusted to approach the signal sparsity gradually. Simulation results verify the efficacies of two proposed methods in the context of wideband spectrum sensing.

The problem of reconstructing a signal waveform when the observed realizations are corrupted by intensive noise and random shifts is considered in this paper. Several ways of performing bispectrum filtering are proposed and investigated. First, it is shown that the signal reconstruction is more efficient if one applies smoothing to the recovered real and imaginary parts of the Fourier spectrum separately instead of filtering the magnitude and phase spectra recovered from a bispectrum estimate. Second, several nonadaptive filters are studied, and it is demonstrated that the proper choice of the filter type and its parameters is critical. Some adaptive filtering techniques based on the Z-parameter and on local polynomial approximation (LPA)-intersection of confidence intervals (ICI) are discussed. The performances of nonadaptive and adaptive filtering techniques in the bispectrum-based signal reconstruction are studied using the mean-squared error as the criterion. It is shown that the use of LPA-ICI and other adaptive filters provides improvement of signal reconstruction in comparison to the conventional bispectrum method and the combined bispectrum filtering methods proposed earlier for nonadaptive filters. The benefits achieved are mainly observed for low (smaller than unity) signal-to-noise ratios.

CT imaging plays a vital role in non-invasive diagnosis and in surgical planning of critical diseases. It is essential to reduce radiation dose during CT imaging as excessive exposure may cause harm to human tissues. To reduce radiation dose, CT image is acquired using limited number of X-ray projections and then to reconstruct the image an adaptive total generalised variation (TGV) minimisation method has been proposed. The simulation results have been compared with the existing TV, TGV and TGV with hard thresholding methods. Typically two types of noises, Gaussian and Poisson distributed noises, are introduced during CT imaging process. So, these two types of noises have been added in measured samples. It is found that after applying soft thresholding and FISTA algorithm with the proposed method, better results have been obtained in noisy imaging environment. The reconstructed CT image quality has been compared using parameters like FSSIM, PSNR, NRMSE and MAE.