Patch-based denoising algorithms aim to reconstruct the clean image patch leaving behind the residual as contaminating noise. The residual should possess statistical properties of contaminating noise. However, it is very likely that the residual patch contains remnants from the clean image patch. In this letter, we propose a new residual correlation based regularization for image denoising. The regularization can effectively render residual patches as uncorrelated as possible. It allows us to derive an analytical solution for sparse coding (atom selection and coefficient calculation). It also leads to a new online dictionary learning update. The clean image is obtained through alternating between the two stages of sparse coding and dictionary updating. The performance of the proposed algorithm is compared with state-of-the-art denoising algorithms in terms of peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and feature similarity index (FSIM), as well as through visual comparison. Experimental results show that the proposed algorithm is highly competitive and often better than leading denoising algorithms. The proposed algorithm is also shown to offer an efficient complement to the benchmark algorithm of block-matching and 3D filtering (BM3D) especially.

A new strategy for multiple structured dictionary learning is proposed. It is motivated by the fact that a signal and its residual after sparse approximation do not necessarily possess the same geometric structure. Based on the geometric structure of each residual component, the most appropriate dictionary is selected. A single-atom sparse representation vector of this residual is calculated and the chosen dictionary is updated. For a given training signal, the process of model (dictionary) selection and one-atom representation is repeated until the desired sparsity or approximation error is reached. Thus, the proposed strategy provides a mechanism whereby each signal can update the most relevant dictionaries based on the structure of its residuals. Simulations conducted over natural images show that, in comparison to standard single or multiple dictionary learning and sparse representation approaches, the proposed strategy significantly improves the representation quality.

In this paper, fuzzy logic enhanced generic color model for fire pixel classification is proposed. The model uses YCbCr color space to separate the luminance from the chrominance more effectively than color spaces such as RGB or rgb. Concepts from fuzzy logic are used to replace existing heuristic rules and make the classification more robust in effectively discriminating fire and fire like colored objects. Further discrimination between fire and non fire pixels are achieved by a statistically derived chrominance model which is expressed as a region in the chrominance plane. The performance of the model is tested on two large sets of images; one set contains fire while the other set contains no fire but has regions similar to fire color. The model achieves up to 99.00% correct fire detection rate with a 9.50% false alarm rate.

In this paper, we propose a real-time fire-detector which combines foreground information with statistical color information to detect fires. The foreground information which is obtained using adaptive background information is verified by the statistical color information to determine whether the detected foreground object is a candidate for fire or not. The output of the both stages is analyzed in consecutive frames which is the verification process of fire that uses the fact that fire never stays stable in visual appearance. The frame processing rate of the detector is about 30 fps with image size of 176times144 which enables the proposed detector to be applied for real-time applications

Facial feature extraction is a fundamental problem in image processing. Correct extraction of features is essential for the success of many applications. Typical feature extraction algorithms fail for low resolution images which do not contain sufficient facial detail. A region-based super-resolution aided facial feature extraction method for low resolution video sequences is described. The region based approach makes use of segmented faces as the region of interest whereby a significant reduction in computational burden of the super-resolution algorithm is achieved. The results indicate that the region-based super-resolution aided extraction algorithm provides significant performance improvement in terms of correct detection in accurately locating the facial feature points.

We derive, via refinable super functions, the characterization of the approximation order of multi-scaling functions in both the time and frequency domains. It is shown that the approximation order is achieved if a linear operator, defined as the difference of the down-sampled convolution matrix and a matrix associated with the super function used, has a zero eigenvalue. The left eigenvectors associated with the zero eigenvalue define the combinations of scaling functions that produce the desired refinable super function. In the frequency domain, the approximation order condition is expressed in terms of the refinement masks of the multi-scaling functions and the refinable super function. It is shown that, implicit in this new characterization, there lie some well known results on approximation order. A matrix equality is derived that equates the presented frequency characterization and Strang's well known characterization of accuracy. It is shown that the approximation order of multi-scaling functions can always be achieved by a refinable, compactly supported super function.

In this work, the phase condition on the scaling filters of two wavelet bases which ensures that the corresponding wavelets are Hilbert transform pairs of each other is studied. An alternative and equivalent phase condition is derived. With the equivalent condition and Fourier series expansions, it is shown that the solution for which the corresponding scaling filters are offset from one another by a half sample is the only solution satisfying the phase condition which results in Hilbert transform pairs of wavelet bases.

A simple method for constructing M-band multi-wavelets using the super function idea is presented. The method is based on formulating the approximation order requirement in terms of a matrix equation and recognizing the generalized left eigenvectors of the matrix Lf a finite portion of the down sampled convolution matrix L as the coefficients that linearly combine to form the desired M-band spline super function with the desired approximation order. Several 3-band multi-wavelets with approximation orders two and three with multiplicity two and three are constructed.

A unified approach for constructing a large class of multi-wavelets is presented. This class includes Geranimo Hardin Massopust, Alpert and Daubechies-like multi-wavelets. The main emphasis is on approximation order of the resulting multi-scaling functions. The unified approach involves formulating the approximation order condition in the framework of super functions and recognizing that the generalized left eigenvectors of the resulting finite down-sampled convolution matrix gives the coefficients that enter the finite linear combination of scaling functions which produces the desired super function from which polynomials of desired degree can be locally approximated.

For multi-wavelets generalized left eigenvectors of the matrix H/sub f/ a finite portion of down-sampled convolution matrix H determine the combinations of scaling functions that produce the desired spline or scaling function from which polynomials of desired degree can be reproduced. This condition is used to construct Alpert's multi-wavelets with multiplicity two, three and four and with approximation orders two, three and four respectively. Higher-multiplicity Alpert multi-wavelets can also be constructed using this new method.

Crosstalk under strong and weak coupling is compared and the two cases are shown to be identical for the important low-frequency range, where the significant components of the input excitation lie. The validity of weak coupling is established in terms of rise time and physical length of interconnects.