Directional Subbands Research Articles

Skin cancer classification leveraging multi-directional compact convolutional neural network ensembles and gabor wavelets

Skin cancer (SC) is an important medical condition that necessitates prompt identification to ensure timely treatment. Although visual evaluation by dermatologists is considered the most reliable method, its efficacy is subjective and laborious. Deep learning-based computer-aided diagnostic (CAD) platforms have become valuable tools for supporting dermatologists. Nevertheless, current CAD tools frequently depend on Convolutional Neural Networks (CNNs) with huge amounts of deep layers and hyperparameters, single CNN model methodologies, large feature space, and exclusively utilise spatial image information, which restricts their effectiveness. This study presents SCaLiNG, an innovative CAD tool specifically developed to address and surpass these constraints. SCaLiNG leverages a collection of three compact CNNs and Gabor Wavelets (GW) to acquire a comprehensive feature vector consisting of spatial–textural–frequency attributes. SCaLiNG gathers a wide range of image details by breaking down these photos into multiple directional sub-bands using GW, and then learning several CNNs using those sub-bands and the original picture. SCaLiNG also combines attributes taken from various CNNs trained with the actual images and subbands derived from GW. This fusion process correspondingly improves diagnostic accuracy due to the thorough representation of attributes. Furthermore, SCaLiNG applies a feature selection approach which further enhances the model’s performance by choosing the most distinguishing features. Experimental findings indicate that SCaLiNG maintains a classification accuracy of 0.9170 in categorising SC subcategories, surpassing conventional single-CNN models. The outstanding performance of SCaLiNG underlines its ability to aid dermatologists in swiftly and precisely recognising and classifying SC, thereby enhancing patient outcomes.

Fingerprint liveness detection based on contourlet, various entropy algorithms and multiobjective genetic algorithm-based ensemble classifier

ABSTRACT Biometric devices have been indicated to be vulnerable to various threats. In the present study, a novel liveness identification technique is introduced according to the noise analysis of fingerprint images. It has been shown that the textural patterns of real fingertips are different from those of spoof fingertips. In this work, Real images were successfully distinguished from fake ones with an accuracy of approximately 99.50%. The database consists of 200 fingerprints, half of which is the real database (i.e. 100 fingerprints), and the other half is the fake database. Textural features are analyzed using pyramidal mean and PDFB analysis techniques that decompose images into directional sub-bands at several scales. The Shannon entropy, approximate entropy, sample entropy, permutation entropy, fuzzy entropy, multiscale entropy, Log energy entropy, and Sure entropy were estimated for all these sub-bands and were arranged into an array. In the classification stage, an ensemble classifier based on a multiobjective genetic algorithm was employed. The results obtained revealed that the suggested technique could successfully differentiate live fingertips from fake ones. The best accuracy was obtained for the proposed ensemble technique, with an average accuracy of 99.52% compared to other classifiers. After the ensemble method, quadratic SVM achieved the best classification performance with a mean accuracy of 97.34% in discriminating real live fingerprints from fake fingerprints. In comparison to other prior techniques, the suggested method produced good classification performance in real-time fingerprint identification while remaining straightforward. Therefore, the system can be a good option for use in real biometric systems.

Neural Contourlet Network for Monocular 360° Depth Estimation

For a monocular 360° image, depth estimation is a challenging because the distortion increases along the latitude. To perceive the distortion, existing methods devote to designing a deep and complex network architecture. In this paper, we provide a new perspective that constructs an interpretable and sparse representation for a 360° image. Considering the importance of the geometric structure in depth estimation, we utilize the contourlet transform to capture an explicit geometric cue in the spectral domain and integrate it with an implicit cue in the spatial domain. Specifically, we propose a neural contourlet network consisting of a convolutional neural network and a contourlet transform branch. In the encoder stage, we design a spatial–spectral fusion module to effectively fuse two types of cues. Contrary to the encoder, we employ the inverse contourlet transform with learned low-pass subbands and band-pass directional subbands to compose the depth in the decoder. Experiments on the three popular 360° panoramic image datasets demonstrate that the proposed approach outperforms the state-of-the-art schemes with faster convergence. Code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/zhijieshen-bjtu/Neural-Contourlet-Network-for-MODE</uri> .

Parameter adaptive unit-linking dual-channel PCNN based infrared and visible image fusion

The properties like pulse synchronization of neurons and global coupling greatly motivated researchers to apply pulse coupled neural network (PCNN) models in accomplishing image fusion. However, manual adjustment of its parameters negatively affects the fusion performance. Moreover, it can process one image at a time. A new parameter adaptive unit-linking dual-channel PCNN model that exhibits all the properties of PCNN and processes two images simultaneously is used in this work to implement a novel fusion algorithm in the non-subsampled contourlet transform (NSCT) domain for the integration of infrared and visible images. At the same time, all the parameters of the proposed model are automatically estimated from the source images. The infrared and visible images are first decomposed using NSCT to provide a sequence of band-pass directional sub-bands and a low-pass sub-band, respectively. The band-pass directional sub-bands are fused using fractal dimension-based linking strength, while the low-pass sub-bands are combined using a new linking strength based on the multi-scale morphological gradient of coefficients. Lastly, the fused image is constructed from the fused sub-bands by applying inverse NSCT. Fourteen state-of-the-art methods are adopted for comparing the performance of the proposed method. The qualitative comparison is done using the human visual system, whereas six objective metrics are considered for the quantitative evaluation. The proposed method is competitive and outperforms some of the existing methods, according to the results of the experiments.

Enhanced JAYA optimization based medical image fusion in adaptive non subsampled shearlet transform domain

Multi-modal image fusion has gained popularity in the medical field as it assists doctors to view the diverse medical image modalities in a single image. The treatment is effectively planned by looking into the fused image that helps doctors diagnose diseases. The medical image fusion aims to merge the texture features from multiple images in a single image. The proposed method includes the application of Adaptive window-based Non-Subsampled Shearlet Transform (ANSST) on source images to separate the low and high-frequency directional sub-bands. Further, an enhanced JAYA (EJAYA) optimization framework is utilized to obtain the adaptive weights for combining high-frequency sub-bands for a multi-modal medical image fusion. The low-frequency bands are fused using the max rule based on the average energy of low-frequency sub-bands. The entire process focuses on preserving the low-frequency band’s energy while improving the texture details in the combined image. In the end, inverse ANSST is applied on merged low-frequency and high-frequency components to get the fused image. Extensive experiments are conducted on data sets obtained from the Brain Atlas website comprising more than 100 images. The significance of the current approach is validated by qualitative and quantitative assessments. The proposed method exhibits good performance in terms of subjective analysis compared to the recent well-known image fusion techniques.

Detection of Alzheimer's disease using features of brain region-of-interest-based individual network constructed with the sMRI image.

Brain networks constructed with regions of interest (ROIs) from the structural magnetic resonance imaging (sMRI) image are widely investigated for detecting Alzheimer's disease (AD). However, the ROI is generally represented by spatial domain-based features, so attentions are hardly paid to constructing a brain network with the frequency domain-based feature. In order to accurately characterize the ROI in the frequency domain and then construct an individual network, in this study, a novel method, which can describe the ROI properly by directional subbands and capture correlations between those ROIs, is proposed to construct a shearlet subband energy feature-based individual network (SSBIN) for AD detection. Specifically, the SSBIN is constructed with 90 ROIs which are segmented from the pre-processed sMRI image based on the automated anatomical labeling atlas, the 90 ROIs are represented by directional subband-based energy feature vectors (SVs) formed by jointing energy features extracted from their directional subbands, and the weight values of the SSBIN are computed by Pearson's correlation coefficient (PCC). Subsequently, two network features are extracted from the SSBIN: the node feature vector (NV) is computed by averaging the 90 SVs; the low dimensional edge feature vector (LV) is obtained by kernel principal component analysis (KPCA). Following that the concatenation of NV and LV is used as a SSBIN-based feature for the sMRI image. Finally, we use support vector machine (SVM) with the radial basis function kernel as classifier to categorize 680 subjects selected from the AD Neuroimaging Initiative (ADNI) database. Experimental results validate that the ROI can be properly characterized by the NV, and correlations between ROIs captured by the LV play an important role in AD detection. Besides, a series of comparisons with four current state-of-the-art approaches demonstrate the higher AD detecting performance of the SSBIN method.

An Automated Brain Image Analysis System for Brain Cancer using Shearlets

In this paper, an Automated Brain Image Analysis (ABIA) system that classifies the Magnetic Resonance Imaging (MRI) of human brain is presented. The classification of MRI images into normal or low grade or high grade plays a vital role for the early diagnosis. The Non-Subsampled Shearlet Transform (NSST) that captures more visual information than conventional wavelet transforms is employed for feature extraction. As the feature space of NSST is very high, a statistical t-test is applied to select the dominant directional sub-bands at each level of NSST decomposition based on sub-band energies. A combination of features that includes Gray Level Co-occurrence Matrix (GLCM) based features, Histograms of Positive Shearlet Coefficients (HPSC), and Histograms of Negative Shearlet Coefficients (HNSC) are estimated. The combined feature set is utilized in the classification phase where a hybrid approach is designed with three classifiers; k-Nearest Neighbor (kNN), Naive Bayes (NB) and Support Vector Machine (SVM) classifiers. The output of individual trained classifiers for a testing input is hybridized to take a final decision. The quantitative results of ABIA system on Repository of Molecular Brain Neoplasia Data (REMBRANDT) database show the overall improved performance in comparison with a single classifier model with accuracy of 99% for normal/abnormal classification and 98% for low and high risk classification.

Infrared maritime small target detection based on edge and local intensity features

In infrared maritime images, small targets are always dim, and there are interferences such as iands and wave clutter. Thus it is easy to miss the real target or generate a large number of false alarms. This paper proposes a detection method based on edge and local intensity features to improve detection accuracy. According to the difference in the similarity of directional edge components between targets and interference, constructing and multiplying directional subbands reduces false alarms. According to the local internal-external intensity features, we designed the candidate target descriptor. The proposed method has higher detection accuracy than several state-of-the-art methods and has stronger parameter robustness through experiments on images with different backgrounds and targets.

The Analysis of Alzheimer's Disease Diagnosis Based on sMRI Slice Image

Morphological networks constructed with structural magnetic resonance imaging (sMRI) images have been widely investigated by exploring interregional alterations of different brain regions of interest (ROI) in the spatial domain for Alzheimer’s disease (AD) classification. However, few attentions are attracted to construct a subband-based individual network with the sMRI image in the frequency domain. In order to verify the feasibility of constructing individual networks with subbands and extract features from the subband-based individual network for AD classification, in this study, we propose a novel method to capture correlations of the abnormal energy distribution patterns related to AD by constructing nonsubsampled contourlet subband-based individual networks (NCSINs) in the frequency domain. Specifically, a 2-dimensional representation of the preprocessed sMRI image is firstly reshaped by downsampling and reconstruction steps. Then, the nonsubsampled contourlet transform is performed on the 2-dimensional representation to obtain directional subbands, and each directional subband at one scale is described by a column energy feature vector (CV) regarded as a node of the NCSIN. Subsequently, edge between any two nodes is weighted with connection strength (CS). Finally, the concatenation of node and edge features of the NCSINs at different scales is used as a network feature of the sMRI image for AD classification. Meanwhile, the support vector machine (SVM) classifier with a radial basis function (RBF) kernel is applied for categorizing 680 subjects from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. Experimental results demonstrate that it is feasible to construct the subband-based individual network in the frequency domain and also show that our NCSIN method outperforms five other state-of-the-art approaches.

The Fusion of Multi-Focus Images Based on the Complex Shearlet Features-Motivated Generative Adversarial Network

The traditional methods for multi-focus image fusion, such as the typical multi-scale geometric analysis theory-based methods, are usually restricted by sparse representation ability and the transferring efficiency of the fusion rules for the captured features. Aiming to integrate the partially focused images into the fully focused image with high quality, the complex shearlet features-motivated generative adversarial network is constructed for multi-focus image fusion in this paper. Different from the popularly used wavelet, contourlet, and shearlet, the complex shearlet provides more flexible multiple scales, anisotropy, and directional sub-bands with the approximate shift invariance. Therefore, the features in complex shearlet domain are more effective. With of help of the generative adversarial network, the whole procedure of multi-focus fusion is modeled to be the process of adversarial learning. Finally, several experiments are implemented and the results prove that the proposed method outperforms the popularly used fusion algorithms in terms of four typical objective metrics and the comparison of visual appearance.

Cryogenic Transport Characteristics of P-Type Gate-All-Around Silicon Nanowire MOSFETs

A 16-nm-Lg p-type Gate-all-around (GAA) silicon nanowire (Si NW) metal oxide semiconductor field effect transistor (MOSFET) was fabricated based on the mainstream bulk fin field-effect transistor (FinFET) technology. The temperature dependence of electrical characteristics for normal MOSFET as well as the quantum transport at cryogenic has been investigated systematically. We demonstrate a good gate-control ability and body effect immunity at cryogenic for the GAA Si NW MOSFETs and observe the transport of two-fold degenerate hole sub-bands in the nanowire (110) channel direction sub-band structure experimentally. In addition, the pronounced ballistic transport characteristics were demonstrated in the GAA Si NW MOSFET. Due to the existence of spacers for the typical MOSFET, the quantum interference was also successfully achieved at lower bias.

Research on Image Fusion Algorithm Based on NSST Frequency Division and Improved LSCN

Single modal medical images provide limited information and cannot reflect all the details of the relevant tissues, which may lead to misdiagnosis in clinical medicine. Therefore, a medical image fusion algorithm based on non-down-sampling shear wave transform (NSST) is proposed. This algorithm fuses multi-modal medical images, enriches the information of fused images, improves the image quality, and provides a basis for clinical diagnosis. Firstly, the low-frequency sub-band and several high-frequency directional sub-bands are obtained by NSST transformation of the source image, and the structural similarity between sub-bands is evaluated. Then, according to the characteristics of low-frequency sub-band images, for sub-images with high similarity, the regional features are obtained by region energy and variance, and the fusion method is based on region feature weighting. For sub-images with low similarity, two images to be fused are input into the LSCN model respectively by fusing the connection items of the improved LSCN model. The improved L-term replaces the ignition frequency in the traditional PCNN as the output. According to the characteristics of high frequency sub-images, the fusion rule of combining visual sensitivity coefficient and regional energy is adopted for sub-images with high similarity. For sub-images with low similarity, an improved guided filter is used to fuse the sub-images in order to maintain the clear edges of the images. Finally, the image is reconstructed by inverse NSST transform. The experimental results show that the proposed algorithm can obtain better fusion effects in both objective and subjective evaluation. The obtained fusion image has rich information, excellent edge retention characteristics, subjectively clear texture and high contrast and good visual effect.

Alzheimer’s disease classification using features extracted from nonsubsampled contourlet subband-based individual networks

Morphological networks constructed with structural magnetic resonance imaging (sMRI) images have been widely investigated by exploring interregional alterations of different brain regions of interest (ROI) in the spatial domain for Alzheimer’s disease (AD) classification. However, few attentions are attracted to construct a subband-based individual network with the sMRI image in the frequency domain. In order to verify the feasibility of constructing individual networks with subbands and extract features from the subband-based individual network for AD classification, in this study, we propose a novel method to capture correlations of the abnormal energy distribution patterns related to AD by constructing nonsubsampled contourlet subband-based individual networks (NCSINs) in the frequency domain. Specifically, a 2-dimensional representation of the preprocessed sMRI image is firstly reshaped by downsampling and reconstruction steps. Then, the nonsubsampled contourlet transform is performed on the 2-dimensional representation to obtain directional subbands, and each directional subband at one scale is described by a column energy feature vector (CV) regarded as a node of the NCSIN. Subsequently, edge between any two nodes is weighted with connection strength (CS). Finally, the concatenation of node and edge features of the NCSINs at different scales is used as a network feature of the sMRI image for AD classification. Meanwhile, the support vector machine (SVM) classifier with a radial basis function (RBF) kernel is applied for categorizing 680 subjects from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. Experimental results demonstrate that it is feasible to construct the subband-based individual network in the frequency domain and also show that our NCSIN method outperforms five other state-of-the-art approaches.

Detection and classification of electroencephalogram signals for epilepsy disease using machine learning methods

AbstractThe electroencephalogram (EEG) signal plays a key role in the diagnosis of epilepsy. This study describes an automated classification of EEG signal for the detection of Epilepsy disease using soft computing methods. The proposed method is comprised of three modules: (a) transformation, (b) feature computation, and (c) feature classifications. In the first module, the nonsubsampled contourlet transform is applied on the EEG signal which decomposes the signal into approximate and directional subbands. The decomposition is done using nonsubsampled pyramid filter bank and nonsubsampled directional filter bank respectively. Secondly, the statistical features are extracted from the decomposed directional subbands using wavelet packet decomposition method. Finally, these features are classified by adaptive neuro‐Fuzzy inference system classification method, which classifies the EEG signal into either focal or nonfocal signal. The proposed method is tested on a set of EEG signals for validation. The average classification rate of the proposed EEG signal classification system is 99.4%. The proposed EEG signal classification methodology achieves a sensitivity of 99.7%, a specificity of 99.7%, and an accuracy of 99.4%. The results confirmed that the proposed method has a potential in the classification of EEG signals and thereby could further improve the diagnosis of epilepsy.

Locally optimum watermark decoder in NSST domain using RSS-based Cauchy distribution

It is important to consider the tradeoff between imperceptibility and robustness requirements in developing an image-watermarking technique, some statistical model-based image watermarking schemes have been designed in the past decade. The effectiveness of a statistical watermark decoder depends highly on the modeling of the transform-domain coefficients and the use of hypothesis testing. In this study, a multiplicative image watermarking scheme is proposed in the nonsubsampled Shearlet transform (NSST) domain, where NSST coefficients are modeled by ranked set sample (RSS) based Cauchy statistical distribution and locally most powerful (LMP) test criterion is applied. Digital image watermarking technique consists of two parts, namely, embedding and extracting. In the embedding process, to achieve relatively good imperceptibility and robustness, watermark data is inserted into the significant NSST directional subband that has the highest energy value, by modifying nonlinearly the significant NSST coefficients. In the extracting phase, a scheme is proposed for designing a blind NSST domain watermark decoder incorporating the RSS based Cauchy statistical distribution and LMP test criterion. Here, the RSS method is used to estimate the location parameter and shape parameter of Cauchy statistical distribution instead of traditional maximum-likelihood (ML) method, which can provide the Cauchy model with higher precision parameters. Experimental results on a set of standard test images show significant improvements in imperceptibility and robustness using the proposed method compared with the best known state-of-the-art approaches.

Infrared and visible image fusion based on nonlinear enhancement and NSST decomposition

In multi-scale geometric analysis (MGA)-based fusion methods for infrared and visible images, adopting the same representation for the two types of images will result in the non-obvious thermal radiation target in the fused image, which can hardly be distinguished from the background. To solve the problem, a novel fusion algorithm based on nonlinear enhancement and non-subsampled shearlet transform (NSST) decomposition is proposed. Firstly, NSST is used to decompose the two source images into low- and high-frequency sub-bands. Then, the wavelet transform (WT) is used to decompose high-frequency sub-bands to obtain approximate sub-bands and directional detail sub-bands. The “average” fusion rule is performed for fusion for approximate sub-bands. And the “max-absolute” fusion rule is performed for fusion for directional detail sub-bands. The inverse WT is used to reconstruct the high-frequency sub-bands. To highlight the thermal radiation target, we construct a non-linear transform function to determine the fusion weight of low-frequency sub-bands, and whose parameters can be further adjusted to meet different fusion requirements. Finally, the inverse NSST is used to reconstruct the fused image. The experimental results show that the proposed method can simultaneously enhance the thermal target in infrared images and preserve the texture details in visible images, and which is competitive with or even superior to the state-of-the-art fusion methods in terms of both visual and quantitative evaluations.

Identification of Alzheimer's disease based on wavelet transformation energy feature of the structural MRI image and NN classifier.

Alzheimer's disease (AD) is now difficult to be identified for clinicians, especially, at its prodromal stage, mild cognitive impairment (MCI), because of no obvious clinical symptom and few impacts on daily life at this phase. In addition, energy distribution differences of brain atrophies reflected in structural magnetic resonance imaging (sMRI) images between MCI patients and older healthy controls (HC) are minimal and subtle, which are difficult to be captured by the spatial analysis. In this study, we propose a novel method (namely AD-WTEF) to identify AD and MCI patients from HC subjects by extracting the wavelet transformation energy feature (WTEF) of the sMRI image. AD-WTEF firstly transforms each scan of the preprocessed sMRI image by wavelet to obtain its directional subbands with the same size at different transformation levels. And then, based on the anatomical automatic labeling (AAL) atlas, AD-WTEF constructs a new brain mask to segment the subbands at the same direction and transformation level into different energy regions of interest (EROIs). Thirdly, by averaging coefficients in an EROI, AD-WTEF gets an energy feature, following that energy features of different EROIs are connected to form an energy feature vector for describing the subbands at the same direction and transformation level. As a result, these energy feature vectors are further concatenated to be a WTEF of the sMRI image. Finally, the nearest neighbor (NN) classifier is selected and used for AD identification. Compared with other seven state-of-the-art methods, our AD-WTEF can effectively identify AD patients using the subtle energy distribution differences of sMRI images. Furthermore, experimental results indicate that our AD-WTEF can also find important brain ROIs related to AD.

An Image Fusion Algorithm based on Modified Contourlet Transform

Multi-focus image fusion has established itself as a useful tool for reducing the amount of raw data and it aims at overcoming imaging cameras’ finite depth of f ield by combining information from multiple images with the same scene. Most of existing fusion algorithms use the method of multi-scale decompositions (MSD) to fuse the s ource images. MSD-based fusion algorithms provide much better performance than the conventional fusion methods .In the image fusion algorithm based on multi-scale decomposition, how to make full use of the characteristics of coefficients to fuse images is a key problem.This paper proposed a modified contourlet transform(MCT) based on wavelets and nonsubsampled directional filter banks(NSDFB). The image is decomposed in wavelet domain,and each highpass subband of wavelets is further decomposed into multiple directional subbands by using NSDFB. The MCT has the important features of directionality and translation invariance. Furthermore, the MCT and a novel region energy strategy are exploited to perform image fusion algorithm. simulation results shows that the proposed method can the fusion results visually and also improve in objective evaluating parameters.

Remote sensing image denoising based on improved semi-soft threshold

Remote sensing image denoising has important applications in aerospace, geophysical exploration and communication engineering. Traditional wavelet transform cannot represent the details and contours of the image texture effectively, because pseudo-Gibbs effect, ringing and blurring of edge details will be produced during de-noising. In this paper, in view of the shortcomings of the existing directional filter design, an eight-direction filter bank that directly decomposes each direction of the image using each directional subband filter is proposed, which is combined with Laplace pyramid transformation to form an optimized contour transformation. A denoising threshold processing algorithm for remote sensing images based on optimized contourlet transformation is proposed. Compared with the traditional denoising method, the improved algorithm has the characteristics of multi-scale and multi-direction, and can better capture the detailed information of the image. The improved semi-soft threshold function is used to process the transformed coefficients, which can better restore the edge information in the image. The results of a series of simulation experiments show that compared with the traditional wavelet threshold function, the contourlet hard threshold function and contourlet soft threshold function, this method achieves better visual effects and higher PSNR (peak signal to noise ratio) while the image is denoised, and the denoising effect is improved by 0.11%. The proposed new threshold function is feasible and can handle the texture information and edge information of remote sensing image well.

Fractal dimension based parameter adaptive dual channel PCNN for multi-focus image fusion

Multi-focus image fusion combines the focused parts of multiple images of the same scene to generate a fully focused image. Dual Channel Pulse coupled neural network (DCPCNN) is frequently used in image fusion framework due to its characteristics like global coupling, pulse synchronization of neurons and simultaneous processing of two images. However, it suffers from the manual setting of its parameters. This paper proposes a transform domain multi-focus image fusion method based on a novel parameter adaptive DCPCNN (PA-DCPCNN) model, in which the parameters are adaptively estimated using the inputs. Moreover, the linking strengths of the PA-DCPCNN model are computed per neuron using a new fractal dimension based focus measure (FDFM). First, the multi-scale and multi-direction decomposition of source images are performed using non-subsampled contourlet transform (NSCT) to obtain the low-pass sub-band and a number of band-pass directional sub-bands. Second, the band-pass directional sub-bands of the source images are fused using the PA-DCPCNN model. Third, the low-pass sub-bands of source images are combined using multi-scale morphological gradient (MSMG) and FDFM to generate the fused low-pass sub-band. Finally, the fused image is obtained by applying inverse NSCT to the fused sub-bands. The performance of the proposed method is compared with fourteen state-of-the-art multi-focus image fusion methods using six objective quality metrics. Experimental results demonstrate that the proposed method is competitive with the state-of-the-art methods in terms of both subjective and objective assessments.