International Journal of Wavelets, Multiresolution and Information Processing

Compared with $l_1$-regularization algorithm, greedy algorithm has great advantage in computational complexity. In this paper, we consider the penalized empirical relaxed greedy algorithm, and analyze its efficiency in the fixed design Gaussian regression problem. Through a careful analysis, we provide the oracle inequalities in the case of finite and infinite dictionary, respectively via choosing appropriate number of greedy iterations. Relying on those oracle inequalities, we obtain the learning rate of the algorithm when the target function lies in the convex hull of the dictionary. Our results show that the error has $O({(\frac{lnn}{n})}^{\frac{1}{2}})$ decay, which is the near optimal convergence rate in the literature.

In this work, a novel design scheme is proposed for the construction of symmetric fractional over-complete wavelet filter banks. We first provide solutions to the open problem of designing low-pass filters that are symmetric and of minimum-length. We then obtain the high high-pass filters via Toeplitz matrix factorization which is of less computational complexity than existing methods. The resulting filter banks are approximately shift-invariant. The designed filter banks are applied in image restoration that uses an analysis based model solved by split Bregman algorithms. The experiments show the constructed symmetric fractional over-complete wavelet transforms (FOWTs) allow better restoration results than some other wavelet transforms in the literature.

Information distortion in regions of image edge is more perceptible for people than those in other regions. To improve the performance on the edge, we present an improved embedded zero-tree wavelet image compression algorithm with weighted sub-block-trees and adaptive coding order. First, we assign bigger weights to the sub-block-trees around image edge. The weights assigned to the sub-blocks in the same spatial location and the same orientation at different scales are equal so that the zero-tree structure of wavelet coefficients is maintained and only a little extra storage is needed. Then we prefer scanning the coefficients on the neighbor of previous significant coefficients and all of them are refined even they are not significant. Adaptive arithmetic coding is applied to the symbols of these coefficients and others respectively. The proposed method pays more attention to the edge and its neighborhood so that the decoded image on the edge is clearer. Compared with similar algorithms, experimental results show that the proposed method can improve the PSNR and SSIM, as well as the subjective visual experience. The proposed method is applicable to any genre of embedded wavelet image codec.

Near real-time monitoring of abrupt changes in satellite time series is important for timely warning of land covers changes. Regression model-based method has been frequently used to detect abrupt change (outlier or anomaly) in time series data. Abrupt change is often determined by residuals test after regression. A simple and widely used residuals test technique is confidence interval (CI), which is often time-independent or constant in many studies. However, satellite time series data is characterized by seasonal variability and periodicity. Although the periodicity could be fitted well by a seasonal-trend regression model, the seasonal variability still remains in the residuals of the regression model. The seasonal variability would lead to less reliable results if abrupt changes are detected by a constant confidence interval (CCI). In order to improve the reliability of abrupt change monitoring in satellite time series, in this paper we develop a criterion namely seasonal confidence interval (SCI) of regression residuals. Experimental evaluations with some simulated and actual satellite time series data demonstrate better performance of the proposed SCI criterion than the CCI criterion for monitoring abrupt changes in satellite time series.

Traditional target detection algorithm based on codebook model only use pixel information of video image while spatial scale information of image is ignored, so the detection result usually has high false detection rate and the target’s characteristics is not obvious. To overcome this difficulty, a novel infrared (IR) moving target detection algorithm based on multiscale codebook model is presented in this paper. The main principle of this algorithm is to make full use of image pixel information and scale information for moving target detection. First, by Gauss pyramid image hierarchical model, the IR video is stratified into three layers, namely the original layer, the second layer and the top layer. Second, background codebook model is built for each layer image, the main feature information is discovered to update background codebook models, and then moving target in IR video is detected according to the updated background model. Finally, the fusion operation is done on detection results of three layers to get the final detection result. Compared with traditional detection algorithm based on codebook model, this IR target detection algorithm combines image pixel information and scale characteristics. By using this novel algorithm, the experiments on some real world IR images are performed. The whole algorithm implementing processes and results are analyzed, and this novel detection algorithm is evaluated from the two aspects: subjective evaluation and objective evaluation. From the experiment results, we can see that the proposed method has better detection effects, richer target information and lower false detection rate.

In this paper, an efficient approximate sparse representation (SR) algorithm with multi-selection strategy is used to solve the image fusion problem. We have shown that the approximate SR is effective for image fusion even if the sparse coefficients are not the sparsest ones possible. A multi-selection strategy is used to accelerate the process of generating the approximate sparse coefficients which are used to guide the fusion of image patches. The relative parameters are also investigated experimentally to further reduce the computational time. The proposed method is compared with some state-of-the-art image fusion approaches on several pairs of multi-source images. The experimental results exhibit that the proposed method is able to yield superior fusion results with less consumption time.

According to the use of normal mouse as an input device to achieve the quick draw of the original handwriting, this paper proposed a quick draw Method of original handwriting based on quadratic Bezier curve. Firstly, the method obtained moving speed and the direction information of the mouse and the information helped to obtain the periphery polygon vertex of the original handwriting drawing. Then Corresponding vertices of a polygon was used to structure the Bezier curve on both sides of the original handwriting to generate the peripheral curve polygon of the original handwriting. Finally, it was input by filling the curve polygon to simulate the user’s handwriting. The experimental results show that the algorithm interacts smoothly and has good simulation effect. Compared with other original handwriting drawing methods with the help of the related electronic input devices, this method only needs the normal mouse instead of stylus and multi touch device to achieve the smooth drawing of original handwriting. Therefore it has wide application value.

In this paper, the recovery of block-sparse signals is considered by the completely perturbed mixed ${\ell }_2/{\ell }_1$ minimization method and a sufficient condition is established to guarantee the robust recovery. The obtained result generalizes the existing result on complete perturbation to the block setting. Specially, we not only improve the condition related to block-restricted isometry property, but also better the error upper bound if the result degenerates to the general case. In addition, some numerical experiments are also carried out to demonstrate the block structure which is an important factor in the process of recovering block-sparse signals, and present outperformance of the mixed ${\ell }_2/{\ell }_1$ minimization method comparing with the ${\ell }_1$ minimization method in the completely perturbed model.

Analysis of seeds is essential for determining seed lot quality and hence its sowing value. Although not fully objective, assessing seed quality with radiographic images has been used as alternative to standard laboratory testing. Here, we applied 2D scale-mixing non-decimated wavelet transform for automatic processing of radiographic images of sunflower seeds. From the transformed images several spectral indices are derived. These descriptors involve spectral slopes which are directly connected with the degree of image regularity. A methodology paradigm was developed to analyze the images and classify each seed as damaged or undamaged (slight, full). By considering binary and multinomial supervised classification, the rate of correct classification was found to be 82% for damaged and full seeds, and 57% for damaged, slightly damaged, and full seeds. Although in principle many different transforms can serve as a basis in deriving spectral indices, this particular transform proved out to be sensitive to image anisotropy (by its scale-mixing nature), and stable in computation (by its non-decimated nature).

It is well-known that the Gabor expansions converge to identity operator in weak* sense on the Wiener amalgam spaces as sampling density tends to infinity. In this paper, we prove the convergence of Gabor expansions to identity operator in the operator norm as well as weak* sense on $W(L^p,{\ell }^q)$ as the sampling density tends to infinity. Also we show the validity of the Janssen’s representation and the Wexler–Raz biorthogonality condition for Gabor frame operator on $W(L^p,{\ell }^q)$.

An efficient lossy compression algorithm for multispectral images based on block Karhunen–Loève transform (KLT) is proposed. First, a two-dimensional discrete wavelet transform is performed on each band of multispectral images to remove the spatial correlation. Subsequently, each band is partitioned into non-overlapping blocks of the same size, and the transform coefficients of each block in the wavelet domain are treated as a single object. Blocks that are co-located in the spectral orientation are affected by an adaptive Karhunen–Loève transform to remove their spectral correlation. Finally, embedded block coding with optimized truncation is performed on all principal components to generate the final bit-stream. Experimental results show that the proposed algorithm, based on block KLT, outperforms the algorithm based on global KLT, without significant increase of complexity.

In research on the navigation and control of an Autonomous Land Vehicle (ALV), the ultrasonic obstacle detection system plays an important role extending the environment cognition capability of the ALV. With a goal of improving the accuracy of ultrasonic obstacle detection, a dynamic data filtering method based on ultrasonic array is presented. The sonar return data is first processed through static filtering according to the geometric relationship of the ultrasonic array. Then, dynamic filtering is executed using the orientation and trajectory information of the vehicle. The dynamic filtering method is compared to the traditional ultrasonic obstacle detection method, which is the static filtering method in a typical field environment. The experiment result demonstrates the validity of the method for solving the fake data problem, and the accuracy of obstacle detection is improved.

Recently, Rashidi-Kouchi et al. devoted their efforts to giving analogs of the Casazza–Christensen general perturbation theorem of Hilbert space frames for the case of g-frames in Hilbert C^*-modules. We found, however, that in the proof they did not obtain the lower bound inequality of g-frames in Hilbert C^*-modules. In this paper, we establish an equivalent definition of g-frames in Hilbert C^*-modules, using it we present a complete proof for the stability result given by them.