The design and adjustment of the divergence in audio applications using nonnegative matrix factorization (NMF) is still open problem. In this study, to deal with this problem, we explore a representation of the divergence using neural networks (NNs). Instead of the divergence, our approach extends the multiplicative update algorithm (MUA), which estimates the NMF parameters, using NNs. The design of the extended MUA incorporates NNs, and the new algorithm is referred to as the deep MUA (DeMUA) for NMF. While the DeMUA represents the algorithm for the NMF, interestingly, the divergence is obtained from the incorporated NN. In addition, we propose theoretical guides to design the incorporated NN such that it can be interpreted as a divergence. By appropriately designing the NN, MUAs based on existing divergences with a single hyper-parameter can be represented by the DeMUA. To train the DeMUA, we applied it to audio denoising and supervised signal separation. Our experimental results show that the proposed architecture can learn the MUA and the divergences in sparse denoising and speech separation tasks and that the MUA based on generalized divergences with multiple parameters shows favorable performances on these tasks.

In this study, Bayesian image denoising, in which the prior distribution is assumed to be a Gaussian Markov random field (GMRF), is considered. Recently, an effective algorithm for Bayesian image denoising with a standard GMRF prior has been proposed, which can help implement the overall procedure and optimize its parameters in O(n)-time, where n is the size of the image. A new GMRF-type prior, referred to as a hierarchical GMRF (HGMRF) prior, is proposed, which is obtained by applying a hierarchical Bayesian approach to the standard GMRF prior; in addition, an effective denoising algorithm based on the HGMRF prior is proposed. The proposed HGMRF method can help implement the overall procedure and optimize its parameters in O(n)-time, as well as the previous GMRF method. The restoration quality of the proposed method is found to be significantly higher than that of the previous GMRF method as well as that of a non-local means filter in several cases. Furthermore, numerical evidence implies that the proposed HGMRF prior is more suitable for the image prior than the standard GMRF prior.

Hyperspectral images (HSIs) are generally susceptible to various noise, such as Gaussian and stripe noise. Recently, numerous denoising algorithms have been proposed to recover the HSIs. However, those approaches cannot use spectral information efficiently and suffer from the weakness of stripe noise removal. Here, we propose a tensor decomposition method with two different constraints to remove the mixed noise from HSIs. For a HSI cube, we first employ the tensor singular value decomposition (t-SVD) to effectively preserve the low-rank information of HSIs. Considering the continuity property of HSIs spectra, we design a simple smoothness constraint by using Tikhonov regularization for tensor decomposition to enhance the denoising performance. Moreover, we also design a new unidirectional total variation (TV) constraint to filter the stripe noise from HSIs. This strategy will achieve better performance for preserving images details than original TV models. The developed method is evaluated on both synthetic and real noisy HSIs, and shows the favorable results.

Motion deblurring for noisy and blurry images is an arduous and fundamental problem in image processing community. The problem is ill-posed as many different pairs of latent image and blur kernel can render the same blurred image, and thus, the optimization of this problem is still unsolved. To tackle it, we present an effective motion deblurring method for noisy and blurry images based on prominent structure and a data-driven heavy-tailed prior of enhanced gradient. Specifically, first, we employ denoising as a preprocess to remove the input image noise, and then restore strong edges for accurate kernel estimation. The image extreme channels-based priors (dark channel prior and bright channel prior) as sparse complementary knowledge are exploited to extract prominent structure. High closeness of the extracted structure to the clear image structure can be obtained via tuning the parameters of extraction function. Next, the integration term of enhanced interim image gradient and clear image heavy-tailed prior is proposed and then embedded into the image restoration model, which favors sharp images over blurry ones. A large number of experiments on both synthetic and real-life images verify the superiority of the proposed method over state-of-the-art algorithms, both qualitatively and quantitatively.

Real-time pulse rate (PR) monitoring based on photoplethysmography (PPG) has been drawn much attention in recent years. However, PPG signal detected under movement is easily affected by random noises, especially motion artifacts (MA), affecting the accuracy of PR estimation. In this paper, a parallel method structure is proposed, which effectively combines wavelet threshold denoising with recursive least squares (RLS) adaptive filtering to remove interference signals, and uses spectral peak tracking algorithm to estimate real-time PR. Furthermore, we propose a parallel structure RLS adaptive filtering to increase the amplitude of spectral peak associated with PR for PR estimation. This method is evaluated by using the PPG datasets of the 2015 IEEE Signal Processing Cup. Experimental results on the 12 training datasets during subjects' walking or running show that the average absolute error (AAE) is 1.08 beats per minute (BPM) and standard deviation (SD) is 1.45 BPM. In addition, the AAE of PR on the 10 testing datasets during subjects' fast running accompanied with wrist movements can reach 2.90 BPM. Furthermore, the results indicate that the proposed approach keeps high estimation accuracy of PPG signal even with strong MA.

For image restoration, an image prior that is obtained from the morphological gradient has been proposed. In the field of mathematical morphology, the optimization of the structuring element (SE) used for this morphological gradient using a genetic algorithm (GA) has also been proposed. In this paper, we introduce a new image prior that is the sum of the morphological gradients and total variation for an image restoration problem to improve the restoration accuracy. The proposed image prior makes it possible to almost match the fitness to a quantitative evaluation such as the mean square error. It also solves the problem of the artifact due to the unsuitability of the SE for the image. An experiment shows the effectiveness of the proposed image restoration method.

Depth (disparity) estimation from a light field (a set of dense multi-view images) is currently attracting much research interest. This paper focuses on how to handle a noisy light field for disparity estimation, because if left as it is, the noise deteriorates the accuracy of estimated disparity maps. Several researchers have worked on this problem, e.g., by introducing disparity cues that are robust to noise. However, it is not easy to break the trade-off between the accuracy and computational speed. To tackle this trade-off, we have integrated a fast denoising scheme in a fast disparity estimation framework that works in the epipolar plane image (EPI) domain. Specifically, we found that a simple 1-D slanted filter is very effective for reducing noise while preserving the underlying structure in an EPI. Moreover, this simple filtering does not require elaborate parameter configurations in accordance with the target noise level. Experimental results including real-world inputs show that our method can achieve good accuracy with much less computational time compared to some state-of-the-art methods.

Edge-preserving smoothing filter smoothes the textures while preserving the information of sharp edges. In image processing, this kind of filter is used as a fundamental process of many applications. In this paper, we propose a new approach for edge-preserving smoothing filter. Our method uses 2D local filter to smooth images and we apply indicator function to restrict the range of filtered pixels for edge-preserving. To define the indicator function, we recalculate the distance between each pixel by using edge information. The nearby pixels in the new domain are used for smoothing. Since our method constrains the pixels used for filtering, its running time is quite fast. We demonstrate the usefulness of our new edge-preserving smoothing method for some applications.

Target recognition in Millimeter-wave Interferometric Synthetic Aperture Radiometer (MMW InSAR) imaging is always a crucial task. However, the recognition performance of conventional algorithms degrades when facing unpredictable noise interference in practical scenarios and information-loss caused by inverse imaging processing of InSAR. These difficulties make it very necessary to develop general-purpose denoising techniques and robust feature extractors for InSAR target recognition. In this paper, we propose a denoising convolutional neural network (D-CNN) and demonstrate its advantage on MMW InSAR automatic target recognition problem. Instead of directly feeding the MMW InSAR image to the CNN, the proposed algorithm utilizes the visibility function samples as the input of the fully connected denoising layer and recasts the target recognition as a data-driven supervised learning task, which learns the robust feature representations from the space-frequency domain. Comparing with traditional methods which act on the MMW InSAR output images, the D-CNN will not be affected by information-loss accused by inverse imaging process. Furthermore, experimental results on the simulated MMW InSAR images dataset illustrate that the D-CNN has superior immunity to noise, and achieves an outstanding performance on the recognition task.

Dai-Yuan (DY) conjugate gradient method is an effective method for solving large-scale unconstrained optimization problems. In this paper, a new DY method, possessing a spectral conjugate parameter βk, is presented. An attractive property of the proposed method is that the search direction generated at each iteration is descent, which is independent of the line search. Global convergence of the proposed method is also established when strong Wolfe conditions are employed. Finally, comparison experiments on impulse noise removal are reported to demonstrate the effectiveness of the proposed method.

In this paper, we propose a novel primary user detection scheme for spectrum sensing in cognitive radio. Inspired by the conventional signal classification approach, the spectrum sensing is translated into a classification problem. On the basis of feature-based classification, the spectral correlation of a second-order cyclostationary analysis is applied as the feature extraction method, whereas a stacked denoising autoencoders network is applied as the classifier. Two training methods for signal detection, interception-based detection and simulation-based detection, are considered, for different prior information and implementation conditions. In an interception-based detection method, inspired by the two-step sensing, we obtain training data from the interception of actual signals after a sophisticated sensing procedure, to achieve detection without priori information. In addition, benefiting from practical training data, this interception-based detection is superior under actual transmission environment conditions. The alternative, a simulation-based detection method utilizes some undisguised parameters of the primary user in the spectrum of interest. Owing to the diversified predetermined training data, simulation-based detection exhibits transcendental robustness against harsh noise environments, although it demands a more complicated classifier network structure. Additionally, for the above-described training methods, we discuss the classifier complexity over implementation conditions and the trade-off between robustness and detection performance. The simulation results show the advantages of the proposed method over conventional spectrum-sensing schemes.

In this letter, an effective low bit-rate image restoration method is proposed, in which image denoising and subspace regression learning are combined. The proposed framework has two parts: image main structure estimation by classical NLM denoising and texture component prediction by subspace joint regression learning. The local regression function are learned from denoised patch to original patch in each subspace, where the corresponding compression image patches are employed to generate anchoring points by the dictionary learning approach. Moreover, we extent Extreme Support Vector Regression (ESVR) as multi-variable nonlinear regression to get more robustness results. Experimental results demonstrate the proposed method achieves favorable performance compared with other leading methods.

In a local region of a color image, the color distribution often takes the form of a linear line in the RGB space. This property is called “Color Line” and we propose a denoising method based on this property. When a noise is added on an image, its color distribution spreads from the Color Line. The denoising is achieved by reducing the spread. In conventional methods, Color Line is assumed to be only a single line, but actual distribution takes various shapes such as a single line, two lines, and a plane and so on. In our method, we estimate the distribution in more detail using plane approximation and denoise each patch by reducing the spread depending on the Color Line types. In this way, we can achieve better denoising results than a conventional method.

In this paper, we consider Bayesian image denoising based on a Gaussian Markov random field (GMRF) model, for which we propose an new algorithm. Our method can solve Bayesian image denoising problems, including hyperparameter estimation, in O(n)-time, where n is the number of pixels in a given image. From the perspective of the order of the computational time, this is a state-of-the-art algorithm for the present problem setting. Moreover, the results of our numerical experiments we show our method is in fact effective in practice.

This paper proposes an image denoising method using singular value decomposition (SVD) with block-rotation-based operations in wavelet domain. First, we decompose a noisy image to some sub-blocks, and use the single-level discrete 2-D wavelet transform to decompose each sub-block into the low-frequency image part and the high-frequency parts. Then, we use SVD and rotation-based SVD with the rank-1 approximation to filter the noise of the different high-frequency parts, and get the denoised sub-blocks. Finally, we reconstruct the sub-block from the low-frequency part and the filtered the high-frequency parts by the inverse wavelet transform, and reorganize each denoised sub-blocks to obtain the final denoised image. Experiments show the effectiveness of this method, compared with relevant methods.

In this paper, a multichannel speech enhancement system which adopts a denoising auto-encoder as part of the beamformer is proposed. The proposed structure of the generalized sidelobe canceller generates enhanced multi-channel signals, instead of merely one channel, to which the following denoising auto-encoder can be applied. Because the beamformer exploits spatial information and compensates for differences in the transfer functions of each channel, the proposed system is expected to resolve the difficulty of modelling relative transfer functions consisting of complex numbers which are hard to model with a denoising auto-encoder. As a result, the modelling capability of the denoising auto-encoder can concentrate on removing the artefacts caused by the beamformer. Unlike conventional beamformers, which combine these artefacts into one channel, they remain separated for each channel in the proposed method. As a result, the denoising auto-encoder can remove the artefacts by referring to other channels. Experimental results prove that the proposed structure is effective for the six-channel data in CHiME, as indicated by improvements in terms of speech enhancement and word error rate in automatic speech recognition.

Mixed noise removal is a major problem in image processing. Different noises have different properties and it is required to use an appropriate removal method for each noise. Therefore, removal of mixed noise needs the combination of removal algorithms for each contained noise. We aim at the removal of the mixed noise composed of Additive White Gaussian Noise (AWGN) and Random-Valued Impulse Noise (RVIN). Many conventional methods cannot remove the mixed noise effectively and may lose image details. In this paper, we propose a new mixed noise removal method utilizing Direction Weighted Median filter (DWM filter) and Block Matching and 3D filtering method (BM3D). Although the combination of the DWM filter for RVIN and BM3D for AWGN removes almost all the mixed noise, it still loses some image details. We find the cause in the miss-detection of the image details as RVIN and solve the problem by re-detection with the difference of an input noisy image and the output by the combination. The re-detection process removes only salient noise which BM3D cannot remove and therefore preserves image details. These processes lead to the high performance removal of the mixed noise while preserving image details. Experimental results show our method obtains denoised images with clearer edges and textures than conventional methods.

Soft-thresholding is a sparse modeling method typically applied to wavelet denoising in statistical signal processing. It is also important in machine learning since it is an essential nature of the well-known LASSO (Least Absolute Shrinkage and Selection Operator). It is known that soft-thresholding, thus, LASSO suffers from a problem of dilemma between sparsity and generalization. This is caused by excessive shrinkage at a sparse representation. There are several methods for improving this problem in the field of signal processing and machine learning. In this paper, we considered to extend and analyze a method of scaling of soft-thresholding estimators. In a setting of non-parametric orthogonal regression problem including discrete wavelet transform, we introduced component-wise and data-dependent scaling that is indeed identical to non-negative garrote. We here considered a case where a parameter value of soft-thresholding is chosen from absolute values of the least squares estimates, by which the model selection problem reduces to the determination of the number of non-zero coefficient estimates. In this case, we firstly derived a risk and construct SURE (Stein's unbiased risk estimator) that can be used for determining the number of non-zero coefficient estimates. We also analyzed some properties of the risk curve and found that our scaling method with the derived SURE is possible to yield a model with low risk and high sparsity compared to a naive soft-thresholding method with SURE. This theoretical speculation was verified by a simple numerical experiment of wavelet denoising.

This paper describes the background noise estimation technique of the tensor product expansion with absolute error (TPE-AE) to estimate multiple sources. The electroencephalogram (EEG) signal produced by the saccadic eye movement is adopted to analyze relationship between a brain function and a human activity. The electrooculogram (EOG) generated by eye movements yields significant problems for the EEG analysis. The denoising of EOG artifacts is important task to perform an accurate analysis. In this paper, the two types of TPE-AE are proposed to estimates EOG and other components in EEG during eye movement. One technique estimates two outer products using median filter based TPE-AE. The another technique uses a reference signal to separate the two sources. We show that the proposed method is effective to estimate and separate two sources in EEG.

In this paper, we introduce a new method to remove random-valued impulse noise in an image. Random-valued impulse noise replaces the pixel value at a random position by a random value. Due to the randomness of the noisy pixel values, it is difficult to detect them by comparison with neighboring pixels, which is used in many conventional methods. Then we improve the recent noise detector which uses a non-local search of similar structure. Next we propose a new noise removal algorithm by sparse representation using DCT basis. Furthermore, the sparse representation can remove impulse noise by using the neighboring similar image patch. This method has much more superior noise removal performance than conventional methods at images. We confirm the effectiveness of the proposed method quantitatively and qualitatively.