nils-herrmann/clean_scirepeval huggingface dataset:
The multiple-parameter discrete fractional Fourier transform

The discrete fractional Fourier transform (DFRFT) is a generalization of the discrete Fourier transform (DFT) with one additional order parameter. In this letter, we extend the DFRFT to have N order parameters, where N is the number of the input data points. The proposed multiple-parameter discrete fractional Fourier transform (MPDFRFT) is shown to have all of the desired properties for fractional transforms. In fact, the MPDFRFT reduces to the DFRFT when all of its order parameters are the same. To show an application example of the MPDFRFT, we exploit its multiple-parameter feature and propose the double random phase encoding in the MPDFRFT domain for encrypting digital data. The proposed encoding scheme in the MPDFRFT domain significantly enhances data security.
A novel block truncation coding of color images by using quaternion-moment-preserving principle

To compress color-pixel blocks, a novel color BTC algorithm, called the quaternion-moment block truncation coding (QMBTC), is presented in this paper. The QMBTC are derived by using the quaternion arithmetic and moment-preserving principle. The proposed color BTC algorithm can adaptively truncate a pixel block into one or two output classes according to the distribution of color values inside the blocks. The experimental results show that the compression ratio will increase as compared with existing color BTC algorithms and the picture quality of reconstructed images is satisfactory.
Adaptive morphology shortest path planning based on rotating object and critical transition point

This paper presents a general approach to find the shortest path for a general moving object with rotation and forward/backward movement among obstacles of arbitrary shapes. We call the object of finding a shortest path by the name of path planning. By utilizing the concept of the critical transition point and adaptive path planning, finding a shortest path problem of car-like vehicles becomes more practical. Moreover, additional efficiency in routing can be obtained since the critical transition point is used in the configuration space. Notice that the computational complexity is not increased. A car-like vehicle model with forward/backward driving and turning mechanism is used to validate the performance of the proposed algorithms. Simulation results show that not only are the proposed algorithms successful in various environments, but also these algorithms have good efficiency in computation. Moreover, routing gains with the help of morphological theory.
Simple effective image and video color correction using quaternion distance metric

Color correction or stabilization methods for image and video are important in signal processing areas. We can obtain image and video with better quality and more pleasing appearance by applying these correction methods. Besides, color corrected image and video also can be used to enhance performance of many post-processing techniques, such as pattern recognition, object tracking, human face matching, etc. In this paper, we have proposed a color correction algorithm based on quaternion algebra for color image and video. First, our method uses quaternion color distance metric to compute the pixel-based color differences between target image (or video frame) and reference image/video frame with similar appearance but slightly different illumination condition. After the color differences of image pixels are obtained, we use these pixels to calculate a correction matrix and use this matrix to correct target image and video frame. Our method can be applied to image and video with fast processing speed and has good performance when compared it with state-of-the-art method in the literature. The algorithm is also simple, effective, and easy to be implemented.
A Secure Compressive Sensing-Based Data Gathering System via Cloud Assistance

Wireless sensors have been helpful and popular for gathering information, in particular in harsh environments. Due to the limit of computation power and energy, compressive sensing has attracted considerable attention in achieving simultaneous sensing and compression of data on the sensor/encoder side with cheap cost. Nevertheless, along with the increase of the data size, the computation overhead for decoding becomes unaffordable on the user/decoder side. To overcome this problem, by taking advantage of resourceful cloud, it is helpful to leverage the overhead. In this paper, we propose a cloud-assisted compressive sensing-based data gathering system with security assurance. Our system, involving three parties of sensor, cloud, and user, possesses several advantages. First, in terms of security, for any two data that are sparse in certain transformed domain, their corresponding ciphertexts are indistinguishable on the cloud side. Second, to avoid the communication bottleneck between the user and cloud, the sensor can encrypt data individually such that, once the cloud receives encrypted data from sensor, it can immediately carry out its task without requesting any information from the user. Third, we show that, even though the cloud knows the permuted support information of data, the security never is sacrificed. Meanwhile, the compression rate can be reduced further. Theoretical and empirical results demonstrate that our system is cost effective and privacy guaranteed and that it possesses acceptable reconstruction quality.
Stable IIR notch filter design with optimal pole placement

This paper presents a two-stage approach for designing an infinite impulse response (IIR) notch filter. First, the numerator of the transfer function of the IIR notch filter is obtained by placing the zeros at the prescribed notch frequencies. Then, the denominator polynomial is determined by using an iterative scheme in which the optimal pole placements are found by solving a standard quadratic programming problem. For stability, the pole radius in the single notch filter design is specified by the designer, and in the multiple notch filter design, the pole radius is constrained by using the implications of Rouche's theorem. Examples are included to illustrate the effectiveness of the proposed techniques.
Closed-form design of maximally flat FIR fractional delay filters

8 types of maximally flat FIR fractional delay filters are proposed. They are designed by separately approximating the real part and the imaginary part of the frequency response. Among these 8 types of filters, two of them are equivalent to the existing design results in the open literature (Samadi, 2004). Therefore, a more general closed-form design of the maximally flat FIR fractional delay filters is described in this paper and some design examples of FIR fractional delay filters are illustrated
Secure image hashing via minimum distortion estimation

Security is still a relatively unexplored issue in image hashing. In this paper, we address this problem and present a new metric, called minimum distortion estimation (MDE), by demonstrating its appropriateness over entropy for secure hashing evaluation. We investigate the relationship between bit changing rate and content distortion via statistical analyses of MDE. This provides a guideline for our design of a new secure image hashing method. The feasibility of our method is further demonstrated via comparisons with two known image hashing methods.
The Wigner distribution of linear time-variant systems

The Wigner distribution relation between the two input and output time-varying spectra of the linear time-variant system is derived. This mathematical relationship can show how a time-variant system modifies the time-varying spectrum of the input to determine that of the output, and this result will be very useful for time-variant filtering in the mixed time-frequency domain. A linear time-variant digital filtering example is used to show the effect of time-variant filtering by using the Wigner distribution.
Video compression based on orthonormal matching pursuits

Video coding schemes based on matching pursuits have been shown to have better coding efficiency and perceptual quality at low bit rates than DCT-based video coding schemes. Matching pursuit is a greedy algorithm that decomposes a signal into a linear combination of bases within an over complete dictionary. However, as the bases are not independent, the redundancy in linear combinations increases as the number of iterations of matching pursuit increases. In this paper, we introduce an orthonormal matching pursuit algorithm that reduces the redundancy between bases and represents a signal by a linear combination of bases more efficiently. Our proposed updated full search matching pursuit algorithm has been shown to be effective in both coding performance and computational complexity. Based on this algorithm, we present an orthonormal matching pursuit video coding scheme that achieves a more efficient coding performance. The coding efficiency and perceptual quality are evaluated and compared to traditional matching pursuit video coding schemes
Split vector-radix-2/8 2-D fast Fourier transform

This letter presents an efficient split vector-radix-2/8 fast Fourier transform (FFT) algorithm. The split vector-radix-2/8 FFT algorithm saves 14% real multiplications and has much lower arithmetic complexity than the split vector-radix-2/4 FFT algorithm. Moreover, this algorithm reduces 25% data loads and stores compared with the split vector-radix-2/4 FFT algorithm.
A Hybrid Coarse/Fine Layered Multicast Scheme Based on Hierarchical Bandwidth Inference Congestion Control

Traditional approaches to receiver-driven layered multicast apply coarse-grain layered congestion control, which enables each receiver to adjust its receiving rate to match the available bandwidth. However, this restricts the scalability of fine-grain scalable video coding. In this paper, we present an approach that facilitates bandwidth inference congestion control in a hybrid coarse/fine layered multicast scheme for multimedia delivery. One-way delay trend detection has proven effective in explicitly or implicitly estimating end-to-end available bandwidth. Using a hierarchical layered probing scheme and a delay trend detection method, we have developed a congestion control protocol for fine-grain layered multicast. Combining this protocol with scalable video coding, we present a framework that achieves efficient scalable video streaming over heterogeneous networks. The performance of our hybrid coarse/fine layered multicast scheme is evaluated by network simulations and the video coding efficiency.
Color Enhancement With Adaptive Illumination Estimation for Low-Backlighted Displays

In this paper, we propose an image enhancement system to maintain human visual perception for low-backlighted LCD or LED displays. Adopting the low-backlight mode can save electrical power and extend battery life. First, we examine the relationship between the image and backlight to maintain visual perceptual quality. Then, we use an adaptive illumination estimation to decompose the image intensity into an illumination layer and a reflectance layer with multiscale and parallel perspectives. We then refer to the given backlight level and our derived image-backlight relationship to compensate the illumination layer and meanwhile enhance the reflectance layer. Finally, we also boost the color saturation. Experiments using both numerical blind/referenceless image spatial quality evaluator and subjective mean opinion score demonstrate that our system outperforms existing systems.
Recursive order-statistic soft morphological filters

A new class of recursive order-statistic soft morphological (ROSSM) filters are proposed and their important properties related to morphological filtering are developed. Criteria for specific selection of parameters are provided to achieve excellent performance in noise reduction and edge preservation. It is shown through experimental results that the ROSSM filters, compared to the order-statistic soft morphological filters or other well known nonlinear filters, have better outcomes in signal reconstruction. Two examples are given for demonstrating the flexibility of the proposed filters in signal processing applications.
Fast OMP: Reformulating OMP via iteratively refining ℓ2-norm solutions

Orthogonal matching pursuit (OMP) is a powerful greedy algorithm in compressed sensing for recovering sparse signals despite its high computational cost for solving large scale problems. Moreover, its theoretic performance analysis based on mutual incoherence property (MIP) is still not accurate enough. To overcome these difficulties, this paper proposes a fast OMP (FOMP) algorithm by reformulating OMP in terms of refining ℓ2-norm solutions in a greedy manner. ℓ2-norm solutions are known for being non-sparse, but we show that the ℓ2-norm solution associated with a greedy structure actually solves the sparse signal reconstruction problem well. We analyze exact recovery of FOMP via an order statistics probabilistic model and provide practical performance bounds.
Symmetric properties of 2-D sequences and their applications for designing quadrantally symmetric linear-phase 2-D FIR digital filters

In this paper, various symmetric and antisymmetric 2-D sequences are used to design quadrantally symmetric/antisymmetric 2-D filters. It is shown that there are sixteen types cases to be considered according to the symmetry/antisymmetry of 2-D sequences in both directions and their filter lengths (even or odd).
3-D FIR Cone-Shaped Filter Design by a Nest of McClellan Transformations and Its Variable Design

In this paper, the technique of a nest of McClellan transformations is proposed for the design of 3-D FIR cone-shaped filters. First, a transformation subfilter for fan-type mapping is found. Then the cosine term of a frequency variable of the above transformation subfilter is replaced by an embedded transformation subfilter which possesses circular contours. The technique stated above is also extended to design 3-D FIR variable cone-shaped filters such that the inclination of the cone-shaped filters can be adjusted online. Moreover, an efficient structure is proposed for the implementation of the designed filters. Several examples will be presented to demonstrate the effectiveness of the proposed method.
Closed-Form Orthogonal Ramanujan Integer Basis

In this letter, a closed-form orthogonal Ramanujan integer basis is proposed and obtained by performing Gram-Schmidt process from the Ramanujan sum and its circular shift. It has a surprisingly simple and sparse form, which is better than the original complete Ramanujan basis. The relationship between the original basis and proposed basis is also clearly illustrated. Therefore, the original basis can be replaced easily.
Robustness Enhancement for Noncentric Quantization-Based Image Watermarking

This paper presents a novel approach for improving the robustness of the quantization-based watermarking scheme. Unlike the conventional approach, which quantizes the host value to the center of the objective interval, the proposed scheme offers the flexibility of determining the quantized value. Given tolerable embedding-induced distortion and the host value, the quantized value can be analytically determined in a closed-form solution, instead of being fixed at the center of the interval. To objectively compare the robustness, different watermarking schemes are implemented in the same distortion-to-noise ratio (DNR) scenario and then the probabilities of error detection are measured. Simulation results indicate that the proposed scheme, compared to the conventional quantization watermarking, could reduce the error probability by 0.113 when DNR is set to 0 dB, whereas the reduction is only 0.037 for the recent Wu's approach. Furthermore, without the finite possible values of the watermarked data, the proposed scheme provides sufficient nondisclosure for the quantization step, whereas in the conventional quantization-based watermarking, the quantization step can be easily inferred from the watermarked data
Discrete Spherical Harmonic Oscillator Transforms on the Cartesian Grids Using Transformation Coefficients

The analog harmonic oscillators are well-studied in quantum physics, including their energy states, wavefunctions, orthogonal properties, and eigenfunctions of the Fourier transform. In addition, the continuous solutions in different dimension and coordinate systems are known. Some discrete equivalents of the 1D wavefunctions were also studied. However, in the 3D spherical coordinate system, the discrete equivalents of the 3D wavefunctions are not established. In this paper, we focus on the spherical harmonic oscillator wavefunctions (SHOWs) the spherical harmonic oscillator transforms (SHOTs), and their discrete implementation. The SHOWs can be synthesized by linear combinations of the Hermite Gaussian functions with proper transformation coefficients. We find that computing the coefficients can be speeded up using the fast Fourier transforms or some recursive relations. These coefficients relate the Hermite transforms with the SHOTs. Some applications of the discrete SHOWs and the discrete SHOTs are introduced. First, the SHOWs are exactly the eigenfunctions of the 3D DFT. Also, the SHOTs can be used to derive the spherical harmonic oscillator descriptor (SHOD), which is a rotational invariant descriptor. We find that the SHOD is not only compatible with the existing rotational descriptors for the spherically sampled data but also outperforms the existing rotational descriptors for 3D Cartesian sampled, bandlimited input data. Besides, the SHOTs can be used to decompose 3D signals into spherical components. Hence, 3D signal reconstruction is done using partially chosen spherical component, and 3D data compression for MRI data is demonstrated using SHOTs for medical applications.
Design of variable fractional-delay 2-D FIR digital filters by weighted least-squares approach

In the paper, the desired response of a variable fractional-delay (VFD) 2-D digital filter is analyzed in detail, and it is found that there are four types of 2-D symmetric/antisymmetric sequences need to be used for the design of VFD 2-D FIR digital filters. Moreover, due to the orthogonality among the approach functions, the four types of 2-D sequences can be determined independently, such that the dimension for each computation can be reduced drasticcally. For simplicity, only the design of odd-odd order VFD 2-D filters are presented in the paper, and the other cases can be achieved in the same manner. To reveal the coefficient characters, the symmetric/antisymmetric properties of filter coefficients and the relationships between coefficients all are tabulated. Also, a design example of nonseparable diamond-shaped low-pass VFD filter is presented to demonstrate the effectiveness of the proposed method.
A general form of 2D Fourier transform eigenfunctions

In this paper, the general form of the two-dimensional Fourier transform (2D FT) eigenfunctions is discussed. It is obtained from the linear combination of the 2D separable Hermite Gaussian functions (SHGFs). For example, the rotated Hermite Gaussian functions (RHGFs) for the rotated coordinate and the Laguerre Gaussian functions (LGFs) for the polar coordinate are two special cases of the general form. With the aid of the general form, we can achieve these 2D functions with perfect orthogonality. Finding the combination coefficients is equivalent to the multinomial expansion problem. Therefore, we can apply the fast Fourier transform and some recurrence relations to the coefficients. The computation cost is much less than the close-form coefficients, which is associated with the Jacobi polynomials.
Fast binary embedding via circulant downsampled matrix

Binary embedding of high-dimensional data aims to produce low-dimensional binary codes while preserving discriminative power. State-of-the-art methods often suffer from high computation and storage costs. We present a simple and fast embedding scheme by first downsampling N-dimensional data into M-dimensional data and then multiplying the data with an M×M circulant matrix. Our method requires O(N + M log M) computation and O(N) storage costs. We prove if data have sparsity, our scheme can achieve similarity-preserving well. Experiments further demonstrate that though our method is cost-effective and fast, it still achieves comparable performance in image applications.
Eigenfilter design of higher-order digital differentiators

An effective approach is proposed for designing higher order differentiators by the eigenfilter method. By minimizing a quadratic measure of the error in the frequency band, an eigenvector of an appropriate matrix is computed to get the filter coefficients. This method is not only simple and fast, but also optimal in the least-squares sense. Comparison to the McClellan-Parks algorithm for minimax equiripple filters shows that both are optimal in the sense of different minimum norms of the error function, but much better performance is obtained with the proposed approach in most of the frequency band, except in the narrowband region near the cutoff edge.
Least-Squares Design of Variable Maximally Linear FIR Differentiators

In this correspondence, the design of variable maximally linear (VML) FIR differentiators by least-squares method is proposed. The VML differentiator is designed such that its maximally flat frequency is adjustable. The used transfer function is formulated in a variable frame, and the Farrow structure can be applied for the implementation of VML FIR differentiators. For comparison, the non-variable optimal design of maximally linear FIR differentiators is also proposed. The experiments show that the variable design indeed possesses the flat characteristics as the independent optimal design.
2D sparse dictionary learning via tensor decomposition

The existing dictionary learning methods mostly focus on ID signals, leading to the disadvantage of incurring overload of memory and computation if the size of training samples is large enough. Recently, 2D dictionary learning paradigm has been validated to save massive memory usage, especially for large-scale problems. To address this issue, we propose novel 2D dictionary learning algorithms based on tensors in this paper. Our learning problem is efficiently solved by CANDECOMP/PARAFAC (CP) decomposition. In addition, our algorithms guarantee sparsity constraint, which makes that sparse representation of the learned dictionary is equivalent to the ground truth. Experimental results confirm the effectness of our methods.
Design of arbitrary FIR log filters by weighted least squares technique

An efficient method to design FIR filters with arbitrary log magnitude and phase responses is proposed. The method is based on an iterative weighted least squares (WLS) approach to obtain a nearly optimal approximation to the given log magnitude function in the least squares sense. The weighting function at each iteration is updated using the result of the previous iteration, which leads to an equiripple approximation in the log magnitude error. The method can be easily modified to approximate arbitrary log complex-valued frequency response, such as complex FIR log filters. Several examples are illustrated to show the effectiveness of the present approach.
Finding the optimal driving path of a car using the modified constrained distance transformation

We propose an algorithm to solve the path planning problem in an automated vehicle guidance system. Many methods have been proposed to solve such a problem, but, none of them takes as many practical factors into consideration. Although the literature dealt with one or more of the above factors separately, none had included them in a single research. We have included the following factors into our model: size and orientation, intended directions, driving costs, and obstacles. A powerful but simple algorithm based on the constrained distance transformation is shown to: (1) determine the feasibility given the start and finish positions; (2) find the optimal collision-free driving path which minimizes the total driving cost subject to the constraints; (3) provide a smooth path.