Image denoising is a critical task in numerous real-world applications. This paper presents an innovative method for image denoising in the wavelet domain, extending the SURELET approach to handle spatially varying noise levels. Traditional methods often assume a constant noise level across the entire image, which is unrealistic in practical scenarios. Our proposed method estimates the noise level locally within small neighborhoods in the wavelet domain, adapting well to images with spatially varying noise. This approach effectively reduces both uniform and spatially varying noise, as demonstrated through extensive experiments on six test images with five distinct noise patterns. The results, evaluated using peak signal-to-noise ratio (PSNR), show that our method outperforms existing denoising techniques, particularly in scenarios with spatially varying noise. This study not only advances the state-of-the-art in image denoising but also highlights the importance of adaptive noise estimation in real-world applications.

Hyperspectral face recognition provides improved classification rates due to its abundant information in the face cubes of every subject in hyperspectral face databases. However, it is less popular in face recognition due to its difficulty in data acquisition, low signal‐to‐noise ratio, and high dimensionality. The authors compare five existing descriptors that are frequently used in 2D face recognition, and use collaborative representation classifier (CRC) with two voting techniques for hyperspectral face recognition. Experimental results demonstrate that, for PolyU‐HSFD database, Gabor filter bank‐based features are very robust to both Gaussian white noise and shot noise, and it achieves very competitive classification results. For CMU‐HSFD database, when the noise level is low, histogram of oriented gradients (HOG) yields good classification results. In addition, when the noise level is high, raw facial images without feature extraction perform very well in term of correct classification rate. The local binary pattern and HOG descriptor are very sensitive to noise even though they achieve rather good classification rates if the facial images contain no noise. The best recognition result for the PolyU‐HSFD is 96.4% ± 2.3 and for the CMU‐HSFD is 98.0% ± 0.7.

Hyperspectral imaging provides new opportunities for improving face recognition accuracy. However, it poses such challenges as difficulty in data acquisition, low signal to noise ratio (SNR), and high dimensionality. In this paper, we propose a novel method for hyperspectral face recognition with good recognition rates. We first reduce noise adaptively from each spectral band and then crop each face according to eye coordinates. We perform minimum noise fraction (MNF) transform to the cropped face data cube in order to extract a number of MNF bands. We perform log-polar transform to each MNF band and extract Fourier spectra from them. In this way, the extracted features are translation-, rotation-, and scale-invariant. We conducted some experiments to test this new method for hyperspectral face recognition with very promising results. For Hong Kong Polytechnic University Hyperspectral Face Database (PolyU-HSPD), we achieved an average correct recognition rate of 92.70% with standard deviation of 2.61 (92.70%±2.61), which is better than 3D Gabor wavelet face recognition (91.30%±2.09), local binary pattern (LBP) classification (90%±2.42), spectral signature-based classification (24.60%±3.87), spectral angle-based classification (25.40%±4.36), and collaborative representation-based classification (CRC) (86.10%±2.37) for this database. When we use all spectral bands in the face dataset, we obtain a correct classification rate of 93.49%±2.53.

Summary Support vector machine (SVM) is one of the most popular classification techniques in pattern recognition community. However, because of outliers in the training samples, SVM tends to perform poorly under such circumstances. In this paper, we borrow the idea from compressive sensing by introducing an extra term to the objective function of the standard SVM in order to achieve a sparse representation. Furthermore, instead of using thel0norm, we adopt thel1norm in our sparse SVM. In most cases, our method achieves higher classification rates than the standard SVM because of sparser support vectors and is more robust to outliers in the datasets. Experimental results show that our proposed SVM is efficient in pattern recognition applications. Copyright © 2015 John Wiley & Sons, Ltd.

In this letter, we study the Ramanujan Sums (RS) transform by means of matrix multiplication. The RS are orthogonal in nature and therefore offer excellent energy conservation capability. The 1-D and 2-D forward RS transforms are easy to calculate, but their inverse transforms are not defined in the literature for non-even function$ ({\rm mod}~ {\rm M}) $. We solved this problem by using matrix multiplication in this letter.

Denoising is a very important preprocessing step in signal/image processing. In this study, a new signal denoising algorithm is proposed by using neighbouring wavelet coefficients. The dual-tree complex wavelet transform is employed because of its property of approximate shift invariance, which is very important in signal denoising. Both translation-invariant (TI) and non-TI versions of the denoising algorithm are considered. Experimental results show that the proposed method outperforms other existing methods in the literature for denoising both artificial and real-life noisy signals.

In this paper, we develop a novel technology that can enhance the spatial resolution of hyperspectral data cube without using any additional images, as would be the case in image fusion. The technology exploits interband spatial misregistration or distortion (often referred to as “keystone”) of the sensor that acquired the data cube and uses it as additional information to increase the spatial resolution of the data cube. Three methods have been developed to derive subpixel-shifted images from the data cube itself in exploiting the sensor's intrinsic characteristics. Two schemes were proposed to organize the derived subpixel-shifted images before being integrated into the high-resolution image using the iterative-back-projection fusion. Experimental results show that the technology can enhance the spatial resolution in the cross-track direction of hyperspectral data cubes by a factor of two.

The denoising of a natural signal/image corrupted by Gaussian white noise is a classical problem in signal/image processing. However, it is still in its infancy to denoise high dimensional data. In this paper, we extended Sendur and Selesnick's bivariate wavelet thresholding from two-dimensional (2D) image denoising to three-dimensional (3D) data cube denoising. Our study shows that bivariate wavelet thresholding is still valid for 3D data cubes. Experimental results show that bivariate wavelet thresholding on 3D data cube is better than performing 2D bivariate wavelet thresholding on every spectral band separately, VisuShrink, and Chen and Zhu's 3-scale denoising.

In this paper, a new denoising method is proposed for hyperspectral data cubes that already have a reasonably good signal-to-noise ratio (SNR) (such as 600 : 1). Given this level of the SNR, the noise level of the data cubes is relatively low. The conventional image denoising methods are likely to remove the fine features of the data cubes during the denoising process. We propose to decorrelate the image information of hyperspectral data cubes from the noise by using principal component analysis (PCA) and removing the noise in the low-energy PCA output channels. The first PCA output channels contain a majority of the total energy of a data cube, and the rest PCA output channels contain a small amount of energy. It is believed that the low-energy channels also contain a large amount of noise. Removing noise in the low-energy PCA output channels will not harm the fine features of the data cubes. A 2-D bivariate wavelet thresholding method is used to remove the noise for low-energy PCA channels, and a 1-D dual-tree complex wavelet transform denoising method is used to remove the noise of the spectrum of each pixel of the data cube. Experimental results demonstrated that the proposed denoising method produces better denoising results than other denoising methods published in the literature.

In this paper, we propose a new nonlinear dimensionality reduction method by combining Locally Linear Embedding (LLE) with Laplacian Eigenmaps, and apply it to hyperspectral data. LLE projects high dimensional data into a low-dimensional Euclidean space while preserving local topological structures. However, it may not keep the relative distance between data points in the dimension-reduced space as in the original data space. Laplacian Eigenmaps, on the other hand, can preserve the locality characteristics in terms of distances between data points. By combining these two methods, a better locality preserving method is created for nonlinear dimensionality reduction. Experiments conducted in this paper confirms the feasibility of the new method for hyperspectral dimensionality reduction. The new method can find the same number of endmembers as PCA and LLE, but it is more accurate than them in terms of endmember location. Moreover, the new method is better than Laplacian Eigenmap alone because it identifies more pure mineral endmembers.

In this paper, we propose a new palmprint classification method by using the contourlet features. The contourlet transform is a new two dimensional extension of the wavelet transform using multiscale and directional filter banks. It can effectively capture smooth contours that are the dominant features in palmprint images. AdaBoost is used as a classifier in the experiments. Experimental results show that the contourlet features are very stable features for invariant palmprint classification, and better classification rates are reported when compared with other existing classification methods.

In this paper, we propose a novel descriptor for invariant pattern recognition by using the Radon transform, the wavelet transform, and the Fourier transform. The Radon transform can capture the directional features of the pattern image by projecting the pattern onto different orientation slices. The combination of the 2-D shift invariant wavelet transform with the Fourier transform can extract features that are invariant to rotation of the patterns. Standard normalization techniques are used to normalize the input pattern image so that it is translation and scale invariant. Experiments conducted in this paper show that the proposed descriptor achieves high recognition rates for different combinations of rotation angles and noise levels. The descriptor is very robust to Gaussian white noise even when the noise level is very high.

A contour-based feature extraction method is proposed by using the dual-tree complex wavelet transform and the Fourier transform. Features are extracted from the 1D signals r and θ, and hence the processing memory and time are reduced. The approximate shift-invariant property of the dual-tree complex wavelet transform and the Fourier transform guarantee that this method is invariant to translation, rotation and scaling. The method is used to recognize aircrafts from different rotation angles and scaling factors. Experimental results show that it achieves better recognition rates than that which uses only the Fourier features and Granlund's method. Its success is due to the desirable shift invariant property of the dual-tree complex wavelet transform, the translation invariant property of the Fourier spectrum, and our new complete representation of the outer contour of the pattern.

A new palmprint classification method is proposed in this paper by using the dual-tree complex wavelet transform. The dual-tree complex wavelet transform has such important properties as the approximate shift-invariance and high directional selectivity. These properties are very important in invariant palmprint classification. Support vector machines are used as a classifier and the Gaussian radial basis function kernel is selected in the experiments. Experimental results show that the dual-tree complex wavelet features outperform the scalar wavelet features, and three previously developed methods. We conclude that the dual-tree complex wavelet features should be used for invariant palmprint classification instead of the scalar wavelet features.

The denoising of a natural image corrupted by Gaussian noise is a classical problem in signal or image processing. Donoho and his coworkers at Stanford pioneered a wavelet denoising scheme by thresholding the wavelet coefficients arising from the standard discrete wavelet transform. This work has been widely used in science and engineering applications. However, this denoising scheme tends to kill too many wavelet coefficients that might contain useful image information. In this paper, we propose one wavelet image thresholding scheme by incorporating neighbouring coefficients, namely NeighShrink. This approach is valid because a large wavelet coefficient will probably have large wavelet coefficients as its neighbours. Experimental results show that NeighShrink is better than the Wiener filter and the conventional wavelet denoising approaches: VisuShrink and SUREShrink. We also investigate different neighbourhood sizes and find that a size of 3/spl times/3 is the best among all window sizes.

Multiwavelets give better results than single wavelets for signal denoising. We study multiwavelet thresholding by incorporating neighboring coefficients. Experimental results show that this approach is better than the conventional approach, which only uses the term-by-term multiwavelet denoising. Also, it outperforms neighbor single wavelet denoising for some standard test signals and real-life images. This is an extension to Cai and Silverman's (see Sankhya: Ind. J. Stat. B, pt.2, vol.63, p.127-148, 2001) work.

Invariance and low dimension of features are of crucial significance in pattern recognition. This paper proposes a novel orthonormal shell Fourier descriptor that satisfies all of these demands. This method first performs orthonormal shell decomposition on the line moment that is obtained from the 2-D pattern, then applies Fourier transform on each scale of the shell coefficients. Unlike other existing wavelet-based methods, our method allows applying common orthonormal wavelets, such as Daubechies, Symmlet and Coiflet, therefore it is simple to implement. We study the structure of the filter used and develop a fast algorithm to rapidly compute the spectra of orthonormal shell coefficients. The complexity of the proposed descriptor is O(n log n). We apply a coarse-to-fine strategy to search the image database; the matching is very quick because of the multiscale feature structure. The effectiveness of this new descriptor is demonstrated by a series of experiments as well as the comparison with other descriptors. The proposed descriptor is robust to white noise.

Feature extraction and pattern classification are two key components in a pattern recognition system. In our approach, each image is represented by a 2D Fourier descriptor which is translation-, rotation-, and scale-invariant. We define a new metric, named the Hellinger-Kakutani metric for measuring the distance between two Fourier descriptors for classification. This metric is filtration-invariant, hence can be used on noisy images. The method is applied to a set of 22 Chinese characters, which contains 7 subsets of similar characters. The rate of accurate recognition is then reported.