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Frames are recognized for their importance in many fields of communications, signal processing, quantum physics, and so on. In this paper, we design an incoherent tight frame by selecting some rows of a matrix that is the Kronecker product of Fourier and unitary matrices. The Kronecker-product-based frame allows its elements to have a small number of phases, regardless of the frame length, which is suitable for low-cost implementation. To obtain the Kronecker-product-based frame with low mutual coherence, we first derive an objective function by transforming the Gram matrix expression to compute the coherence. If the Hadamard matrix is employed as a unitary matrix, the objective function can be computed efficiently with low complexity. Then, we find a subsampling index set for the Kronecker-product-based frame by minimizing the objective function. In simulations, we show that the Kronecker-product-based frames can achieve similar mutual coherence to optimized harmonic frames of a large number of phases. We apply the frames to compressed sensing (CS) as the measurement matrices, where the Kronecker-product-based frames demonstrate reliable performance of sparse signal recovery. [ABSTRACT FROM AUTHOR]

The compressive sensing method is an effective way of under-sampling array signal processing, and the measurement matrix is a key technology of compressive sensing processing, which is of decisive significance to improve the performance of under-sampling array signal processing. In this paper, an under-sampling array signal processing method based on an improved Hadamard measurement matrix was proposed. This method improved the construction of the measurement matrix by a compressing zero method capable of reducing the redundant data, enhancing the non-correlation between columns, improving the RIP condition, and improving the performance of the compressive sensing method. The performance was verified by simulation and real data from the lake, and the results showed that the method proposed in this paper has obvious performance advantages compared with the Toeplitz Circular Matrix, the m-sequence-based matrix, and the partial Hadamard matrix under the same conditions. [ABSTRACT FROM AUTHOR]

Authentication of the digital image has much attention for the digital revolution. Digital image authentication can be verified with image watermarking and image encryption schemes. These schemes are widely used to protect images against forgery attacks, and they are useful for protecting copyright and rightful ownership. Depending on the desirable applications, several image encryption and watermarking schemes have been proposed to moderate this attention. This framework presents a new scheme that combines a Walsh Hadamard Transform (WHT)-based image watermarking scheme with an image encryption scheme based on Double Random Phase Encoding (DRPE). First, on the sender side, the secret medical image is encrypted using DRPE. Then the encrypted image is watermarking based on WHT. The combination between watermarking and encryption increases the security and robustness of transmitting an image. The performance evaluation of the proposed scheme is obtained by testing Structural Similarity Index (SSIM), Peak Signal-to-Noise Ratio (PSNR), Normalized cross-correlation (NC), and Feature Similarity Index (FSIM). [ABSTRACT FROM AUTHOR]

This paper proposes a novel image compression‐encryption scheme based on compressive sensing and bit‐level XOR. In the proposed scheme, the encrypted sequences are generated from a 4‐D hyper‐chaotic Lorenz system and a Logistic system. First, an original image is sampled by a secure block parallel compressive sensing (PCS) scheme. In the PCS phase, a key‐controlled discrete cosine transform sparse basis matrix and a key‐controlled complex Hadamard measurement matrix are employed. Next, the real part and imaginary part of the resulting complex‐valued data are quantized and transformed into bit streams, respectively. After that, the two generated bit streams are combined into one bit stream. Then, the resulting bit stream is further encrypted by a bit‐level XOR operation, where the encrypted key is generated from a chaotic system. The experiment results show the effectiveness and reliability of the proposed joint compression‐encryption scheme. The proposed scheme can not only enhance the security of the compressed image but also improve the reconstructed quality of the compressed image. [ABSTRACT FROM AUTHOR]

Multicarrier waveforms with enhanced spectral efficiency, low latency, and high throughput are required for 5G wireless networks. The Orthogonal Frequency Division Multiplexing (OFDM) method is well-known in research, but due to its limited spectral efficiency, various alternative waveforms are being considered for 5G systems. In the recent communication world, NOMA (non-orthogonal multiple access) plays a significant part due to its wider transmission of data with less bandwidth allocation. Even if a high data rate can be attained, the transmission problem will arise due to the spread of multiple paths. In order to reduce complexity and area utilization, a novel PL-based FWFT (Fast walsh hadamard fourier transform) technique is proposed and implemented in the VLSI architecture. To achieve a high-performance system, the main concept of pass transistor logic (PL) with VLSI implementation is to diminish the size and power consumption. Finally, the performance of the proposed FWFT/IFWFT implementation has been evaluated. For FPGA's 16-point FWFT, the number of transistors decreased by 21% and the total power required was reduced by 5.5%. The same implementation for 34 transistor-pass-logic customs and power consumption is 2.764 mW with a latency of 78.256 ns. As a consequence, the proposed system achieves low power, area and low complexity system that can enhance the function of the multicarrier waveform systems. [ABSTRACT FROM AUTHOR]

This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concepts. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the Hadamard matrix product. Thereby, some standard results arising for Max-Times systems with nonnegative entries appear as a special case. The case of two sided systems is also analyzed. In addition, a notion of eigenvalue in limit is considered. It is shown that one can construct a special semi-continuous regularized polynomial whose zeros are related to the eigenvalues of a matrix with nonnegative entries. [ABSTRACT FROM AUTHOR]

Using a concatenated construction for -ary codes, we construct codes over in the Lee metrics which after a proper mapping to the binary alphabet (which in the case of is the well-known Gray map) become binary Hadamard codes (in particular, Hadamard matrices). Our construction allows to increase the rank and the kernel dimension of the resulting Hadamard code. Using computer search, we construct new nonequivalent Hadamard matrices of orders , , and with various fixed values of the rank and the kernel dimension in the range of possible values. It was found that in a special case, our construction coincides with the Kronecker (or Sylvester) construction and can be regarded as a version of a presently known [1] modified Sylvester construction which uses one Hadamard matrix of order and (not necessarily distinct) Hadamard matrices of order . We generalize this modified construction by proposing a more general Sylvester-type construction based on two families of (not necessarily distinct) Hadamard matrices, namely, on matrices of order and matrices of order . The resulting matrix is of order , as in the construction from [1]. [ABSTRACT FROM AUTHOR]

We prove the Johnson-Lindenstrauss property for matrices ΦDξ, where Φ has the restricted isometry property and Dξ is a diagonal matrix containing the entries of a Kronecker product ξ=ξ(1)⊕...⊕ξ(d) of d independent Rademacher vectors. Such embeddings have been proposed in recent works for a number of applications concerning compression of tensor structured data, including the oblivious sketching procedure by Ahle et al. for approximate tensor computations. For preserving the norms of p points simultaneously, our result requires Φ to have the restricted isometry property for sparsity C(d)(logp)d. In the case of subsampled Hadamard matrices, this can improve the dependence of the embedding dimension on p to (logp)d while the best previously known result required (logp)d+1. That is, for the case of d=2 at the core of the oblivious sketching procedure by Ahle et al., the scaling improves from cubic to quadratic. We provide a counterexample to prove that the scaling established in our result is optimal under mild assumptions. [ABSTRACT FROM AUTHOR]

Cancelable biometrics is a powerful remedy for information leakage caused by the extensive usage of unprotected biometric data. Current measures usually suffer from deteriorated accuracy, which is known as the security–performance tradeoff. Motivated by these concerns, in this article, a novel cancelable fingerprint approach, i.e., Indexing-Min–Max (IMM) hashing, is proposed to securely transform a fixed-length fingerprint feature vector to a discrete index hashed code. IMM hashing is essentially established upon the min–max hash and further strengthened by the integration of the partial Hadamard transform, which alleviates performance deterioration while maintaining a high security level. Extensive experiments on FVC2002 and FVC2004 fingerprint datasets coupled with comprehensive theoretical analyses demonstrate the favorable accuracy and strong anti-attack resilience of the proposed method. Besides, compared to the unprotected counterpart, the matching precision of the protected templates yields little accuracy loss or even improved performance, which means the security–performance tradeoff is well handled. Furthermore, IMM hashing also meets the unlinkability and revocability requisites of cancelable biometrics. [ABSTRACT FROM AUTHOR]

Hadamard fractional calculus is one of the most important fractional calculus theories. Compared with a single Hadamard fractional order equation, Hadamard fractional differential equations have a more complex structure and a wide range of applications. It is difficult and challenging to study the dynamic behavior of Hadamard fractional differential equations. This manuscript mainly deals with the boundary value problem (BVP) of a nonlinear coupled Hadamard fractional system involving fractional derivative impulses. By applying nonlinear alternative of Leray-Schauder, we find some new conditions for the existence of solutions to this nonlinear coupled Hadamard fractional system. Our findings reveal that the impulsive function and its impulsive point have a great influence on the existence of the solution. As an application, we discuss an interesting example to verify the correctness and validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, firstly, Hermite-Hadamard inequality via s-convex functions in the second sense using Caputo-Fabrizio fractional integral operator is established. We also compare our results with the existing ones. It is also shown that the obtained results are a generalization of the existing results. Finally, we give their applications to special means. [ABSTRACT FROM AUTHOR]

Over the past few years, image emotion classification (IEC) has received increasing research interest. Existing works usually define IEC as a multi-class classification problem from features to emotions, while the subjectivity of user perception is often ignored. However, our experimental study shows that there are coupling relationships between users and emotions, as well as users and features. To address such issues, in this paper, we propose a new IEC model, called CoupledIEC. In CoupledIEC, to capture the user-emotion coupling, a clustering-based embedding model is proposed to encode users of similar emotion preferences with close representations. To model the user-feature coupling, a convolutional neural network-based coupling learning model is developed, where the Hadamard product and the matrix product are employed respectively to capture the explicit and the implicit user-feature coupling information. The two models are then integrated in a unified neural network. The experimental results on real-world image collection demonstrate that the IEC performance can be improved significantly by taking into account user-emotion and user-feature couplings. [ABSTRACT FROM AUTHOR]

In this paper, we show that applying a machine learning technique called auto-decoder (AD) to high-rate and short length Reed–Muller (RM) decoding enables it to achieve maximum likelihood decoding (MLD) performance and faster decoding speed than when fast Hadamard transform (FHT) is applied in additive white Gaussian noise (AWGN) channels. The decoding speed is approximately 1.8 times and 125 times faster than the FHT decoding for R (1 , 4) and R (2 , 4) , respectively. The number of nodes in the hidden layer of AD is larger than that of the input layer, unlike the conventional auto-encoder (AE). Two ADs are combined in parallel and merged together, and then cascaded to one fully connected layer to improve the bit error rate (BER) performance of the code. [ABSTRACT FROM AUTHOR]

Radio frequency interference (RFI) is a significant challenge for high-sensitivity phased array instruments. RFI can be suppressed using digital signal processing, but to improve dynamic range for wideband RFI, it can be desirable to remove interference in the analog domain before sampling. In previous work, it has been shown that analog true time delay (TTD) stages with a truncated Hadamard transform can place a wide-band spatial null on RFI from a given direction of arrival. We show that TTD and Hadamard projection is mathematically equivalent to a bank of classical narrow-band subspace projection beamformers, but with a structure that allows efficient implementation in either analog circuitry or digital hardware. We analyze how loss in the TTD blocks and time delay errors affect beamformer performance and propose methods for calibrating time delays. Simulation results show that ideal TTD and Hadamard projection matches the bank of subspace projection beamformers and places deep nulls over wideband RFI signals while achieving SNR performance comparable to the maximum signal-to-interference and -noise ratio beamformer. [ABSTRACT FROM AUTHOR]

This paper presents a novel scheme based on the Crosstalk Harnessed Signaling (CHS) technique for parallel high-speed interfaces. The proposed scheme, called Asymmetric Crosstalk Harnessed Signaling (ACHS), provides a robust and consistent eye opening for all the transmitted bits in the interface. The Hadamard matrix employed for CHS encoding has been modified to a non-square format in order to either eliminate the common eigenmode or turn it differential. This in turn results in a signaling scheme that converts a binary data array to a slightly larger signal/interconnect array. The resulting signaling and routing overhead translates into a comparable eye opening across all the bits inside the encoded bus, overcoming the crosstalk sensitivity associated to the common mode present in the original CHS scheme. Both CHS and the proposed ACHS are implemented on a 16-bit source-synchronous bus wired through 3-dimensional interconnect arrangements in a multi-stripline stackup, in order to compare performances in very aggressive crosstalk environments. Simulation results show a consistent eye opening across all data bits when ACHS is applied, rendering a fully functional bus with only 11% routing overhead, against a practically inoperable bus in the CHS case, due to the eye collapse for the common-mode encoded bit. [ABSTRACT FROM AUTHOR]

One of the critical challenges in multicarrier‐based systems is peak to average power ratio (PAPR). Recently, Filter Bank Multicarrier (FBMC) is proved to be a promising candidate that can replace the traditional orthogonal multiplexing division (OFDM) scheme due to its better spectral efficiency, reducing both inter‐channel interference (ICI) and PAPR. Due to their advantages in reducing the PAPR without impacting the BER, the Hadamard transform was used in the proposed FBMC based VLC system. Furthermore, here, the discreet cosine transform (DCT) precoding is also used to boost the potential for PAPR reduction and the BER efficiency. The negative signals are not clipped off as in traditional asymmetrically‐clipped optical OFDM (ACO‐OFDM) signals to reduce the impact of large‐amplitude signal reduction nor add dc biasing for cancelling negative signals as in traditional DC‐biased optical OFDM (DCO‐OFDM) signals. Furthermore, a Clipping ratio is introduced to allow a trade‐off between bit error rate (BER) and PAPR reduction, and the optimal PAPR reduction is investigated. The obtained results show that the proposed FBMC based VLC system with DCT and clipping technique can reduce the PAPR and achieve good BER efficiency compared to the OFDM based VLC system. [ABSTRACT FROM AUTHOR]

The accuracy and stability of navigation algorithms are crucial preconditions for underwater gravity matching aided navigation. To improve the matching accuracy and robustness of the matching algorithm, this paper presents a novel gravity matching navigation algorithm based on multiscale search and Hadamard transformed difference. The Hadamard transformation process was first time introduced in the new algorithm for the Walsh–Hadamard kernel function with the property of energy conservation. The gravity measurement sequences could be converted to the Hadamard domain; thus, the difference in numerical values, tendency, and spatial structure of the gravity measurement sequence were also a focus in the new algorithm, whereas only gravity statistical values were considered in classical matching algorithms. Therefore, with the proposed algorithm, the number of measurements necessary for matching can be effectively reduced, while improving the matching accuracy and success rate. In addition, a multiscale neighborhood search strategy based on contour constraints was designed to improve the matching efficiency, whereas a point-by-point global search was widely used in classical matching algorithms. Marine gravity maps of the South China Sea were used to construct the simulation tests. Simulation results show that under various conditions, the new algorithm has lower requirements for the number of measurements, measuring accuracy, and matching areas while exhibiting a higher navigation accuracy, matching success rate, and matching efficiency. Thus, the proposed algorithm could provide a new option for future practical applications of gravity matching aided navigation. • The Hadamard transformation was introduced in the gravity matching aided navigation. • A multiscale neighborhood search strategy based on contour constraints was designed. • The proposed method has better navigation accuracy, robustness, and efficiency in simulation tests. • The new algorithm has lower requirements for the number of measurements, measuring accuracy and matching areas. [ABSTRACT FROM AUTHOR]

Next-generation invasive neural interfaces require fully implantable wireless systems that can record from a large number of channels simultaneously. However, transferring the recorded data from the implant to an external receiver emerges as a significant challenge due to the high throughput. To address this challenge, this article presents a neural recording system-on-chip that achieves high resource and wireless bandwidth efficiency by employing on-chip feature extraction. Energy–area-efficient 10-bit 20-kS/s front end amplifies and digitizes the neural signals within the local field potential (LFP) and action potential (AP) bands. The raw data from each channel are decomposed into spectral features using a compressed Hadamard transform (CHT) processor. The selection of the features to be computed is tailored through a machine learning algorithm such that the overall data rate is reduced by 80% without compromising classification performance. Moreover, the CHT feature extractor allows waveform reconstruction on the receiver side for monitoring or additional post-processing. The proposed approach was validated through in vivo and off-line experiments. The prototype fabricated in 65-nm CMOS also includes wireless power and data receiver blocks to demonstrate the energy and area efficiency of the complete system. The overall signal chain consumes 2.6 $\mu \text{W}$ and occupies 0.021 mm2 per channel, pointing toward its feasibility for 1000-channel single-die neural recording systems. [ABSTRACT FROM AUTHOR]

The cyclicity index of a matrix is the cyclicity index of its critical subgraph, namely, the subgraph of the adjacency graph which consists of all cycles of the maximal average weight. The cyclicity index of a graph is the least common multiple of the cyclicity indices of all its maximal strongly connected subgraphs, and the cyclicity index of a strongly connected graph is the least common divisor of the lengths of its (directed) cycles. In this paper we obtain the characterization of linear, possibly non-surjective, transformations of tropical matrices preserving the cyclicity index. It appears that non-bijective maps with these properties exist and all maps are exhausted by transposition, renumbering of vertices, Hadamard multiplication with a matrix of a certain special structure, and certain diagonal transformation. Moreover, only diagonal transformation can be non-bijective. [ABSTRACT FROM AUTHOR]

Rationale: Multiplexing ion mobility spectrometry with multiple ion injection pulses was used to achieve a high duty cycle and thus improve the signal‐to‐noise (S/N) ratio while maintaining high resolving power compared with the traditional single‐pulse signal averaging method. Historically, an ion mobility spectrum was reconstructed by various multiplexing methods including Fourier transform ion mobility spectrometry (FT‐IMS), Hadamard transform ion mobility spectrometry (HT‐IMS), and linear frequency modulation correlation ion mobility spectrometry (LFM‐CIMS) sequence or Barker code. Methods: To achieve an artifact‐free multiplexing ion mobility spectrum, an almost perfect sequence (APS) with correlation technique was proposed to modulate the Bradbury‐Nielson ion gate and was compared with FT‐IMS, HT‐IMS, LFM‐IMS, and the traditional single‐pulse signal averaging method. Results: Experimental results showed that there are no artifact peaks in the APS‐IMS spectra except an inverted mirror peak, and the S/N ratio was improved 5–8 times with a repetition time of 40–60 ms, corresponding to the improvement in the duty cycle. With the same duty cycle and similar acquisition time, APS‐IMS showed a higher S/N ratio than HT‐IMS for its unique autocorrelation response. Conclusions: The APS‐IMS technique offered a higher duty cycle and relatively shorter modulation period compared with reported multiplexing methods and is suitable to track rapidly changing signals without losing information and adding extra transformation artifact peaks. [ABSTRACT FROM AUTHOR]

Due to advantages such as the high efficiency of light utilization, small volume, and vibration resistance, digital micro-mirror device (DMD)-based spectrometers are widely used in ocean investigations, mountain surveys, and other field science research. In order to eliminate the stray light caused by DMDs, the stray light in DMD-based spectrometers was first measured and analyzed. Then, the stray light was classified into wavelength-related components and wavelength-unrelated components. Moreover, the noise caused by the stray light was analyzed from the perspective of encoding equation, and the de-noising decoding equation was deduced. The results showed that the accuracy range of absorbance was enhanced from [0, 1.9] to [0, 3.1] in single-stripe mode and the accuracy range of absorbance was enhanced from [0, 3.8] to [0, 6.3] in Hadamard transform (HT) multiple-stripe mode. A conclusion can be drawn that the de-noising strategy is feasible and effective for enhancing the SNR in DMD-based spectrometers. [ABSTRACT FROM AUTHOR]

An improved power-only measurement method is proposed to calibrate phased arrays, which is aimed at solving two remaining problems: little contribution of one antenna element's phase shifting to the whole array's power and the ambiguity of solutions. The method includes four steps. Firstly, the random distributed phase of each element is adjusted to guarantee that it is −90° to +90° relative to the reference element. Secondly, the proper number of the elements shifting their phases together is approximately determined. Then, an invertible matrix is formed from the standard Hadamard matrix to split the array into different groups, which applies to an arbitrary number of elements; Finally, the array gets calibrated with an existing method. Numerical simulations and experiments are conducted to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We propose a method for imaging a periodic moving/state-changed object based on computational ghost imaging with Hadamard speckle patterns and a slow bucket detector, named as PO-HCGI. In the scheme, speckle patterns are produced from a part of each row of a Hadamard matrix. Then, in each cycle, multiple speckle patterns are projected onto the periodic moving/state-changed object, and a bucket detector with a slow sampling rate records the total intensities reflected from the object as one measurement. With a series of measurements, the frames of the moving/state-changed object can be obtained directly by the second-order correlation function based on the Hadamard matrix and the corresponding bucket detector measurement results. The experimental and simulation results demonstrate the validity of the PO-HCGI. To the best of our knowledge, PO-HCGI is the first scheme that can image a fast periodic moving/state-changed object by computational ghost imaging with a slow bucket detector. [ABSTRACT FROM AUTHOR]

By utilizing the non-maximally entangled four-qubit cluster states as the quantum channel, we first propose a hierarchical quantum information splitting scheme of arbitrary three-qubit states among three agents with a certain probability. Then we generalize the scheme to arbitrary multi-qubit states. Hierarchy is reflected on the different abilities of agents to restore the target state. The high-grade agent only needs the help of one low-grade agent, while the low-grade agent requires all the other agents' assistance. The designated receiver performs positive operator-valued measurement (POVM) which is elaborately constructed with the aid of Hadamard matrix. It is worth mentioning that a general expression of recovery operation is derived to disclose the relationship with measurement outcomes. Moreover, the scheme is extended to multiple agents by means of the symmetry of cluster states. [ABSTRACT FROM AUTHOR]

In this research, a new class of fractional boundary value problems is introduced and studied, which combine Hilfer fractional derivatives with iterated Riemann-Liouville and Hadamard fractional integrals boundary conditions. Existence and uniqueness results are obtained by using standard tools from fixed point theory. The obtained results are well illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this work, we define the Hadamard-type product of two polynomials by the aid of the Hadamard product of two polynomials. Then we obtain the Hadamard-type k-step Fibonacci sequence by using Hadamard-type product of characteristic polynomials of the Fibonacci sequence and the k-step Fibonacci sequence. Also, we derive relationships between the Hadamard-type k-step Fibonacci sequences and the generating matrices for these sequences. Finally, we give some properties of these sequences such as the Binet formula, the combinatorial representations, the generating function, the exponential representation. [ABSTRACT FROM AUTHOR]

Optimal experimental design (OED) is the general formalism of sensor placement and decisions about the data collection strategy for engineered or natural experiments. This approach is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, and environmental and urban studies. State-of-the-art computational methods for experimental design, however, do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines or radar and satellite retrievals. Discarding evident data correlations leads to biased results, poor data collection decisions, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted likelihood and is valid for both finite- and infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach by using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain. [ABSTRACT FROM AUTHOR]

We propose new variants of the sketch-and-project method for solving large scale ridge regression problems. First, we propose a new momentum alternative and provide a theorem showing it can speed up the convergence of sketch-and-project, through a fast sublinear convergence rate. We carefully delimit under what settings this new sublinear rate is faster than the previously known linear rate of convergence of sketch-and-project without momentum. Second, we consider combining the sketch-and-project method with new modern sketching methods such as Count sketch, SubCount sketch (a new method we propose), and subsampled Hadamard transforms. We show experimentally that when combined with the sketch-and-project method, the (Sub)Count sketch is very effective on sparse data and the standard Subsample sketch is effective on dense data. Indeed, we show that these sketching methods, combined with our new momentum scheme, result in methods that are competitive even when compared to the conjugate gradient method on real large scale data. On the contrary, we show the subsampled Hadamard transform does not perform well in this setting, despite the use of fast Hadamard transforms, and nor do recently proposed acceleration schemes work well in practice. To support all of our experimental findings, and invite the community to validate and extend our results, with this paper we are also releasing an open source software package: RidgeSketch. We designed this object-oriented package in Python for testing sketch-andproject methods and benchmarking ridge regression solvers. RidgeSketch is highly modular, and new sketching methods can easily be added as subclasses. We provide code snippets of our package in the appendix. [ABSTRACT FROM AUTHOR]

Electroencephalographic (EEG) and electromyography (EMG) signal classification seem to be a modulus topic in engineering and the medical field. The nature of the EEG and EMG signal is non‐stationary, noisy and high dimensional. The intrusion of noise in the signal may distress movement recognition. A novel methodology is being developed in this research to deal with these issues. Here, the EEG and EMG signals are recorded using the BCI2000 system. The proposed model comprises three phases: pre‐processing, feature extraction (FE), and motion classification. The pre‐processing method can be used to enhance visual appearances and the quality of the signal. The hybrid discrete wavelet based delayed error normalized least mean square error (DWT‐DENLMS) is introduced to eliminate the presence of motion artifacts in the recorded EEG and EMG signal. After pre‐processing, the recorded signals are combined and forwarded to the FE stage. The hybrid Dual tree complex wavelet transforms based on Walsh Hadamard transform (DTCWT‐WHT) is proposed to extract the indispensable time domain features from the combined biological signal. The hybrid capsule transient autoencoder (HCTAE) algorithm is proposed to classify the motion recognition (T0‐rest, T1‐left fist and both fists, and T2‐right fist, both feet). The error in the network model is diminished by transient search optimization (TSO) strategy. The Python platform is used to implement the developed approach, and the performance of the optimized classification approach yields accuracy, precision, recall, F1 score and specificity of 98.51%, 97.25%, 97.94%, 97.58% and 98.94%, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a switching for 2-designs, which defines a type of trade. We illustrate this method by applying it to some symmetric (64, 28, 12) designs, showing that the switching introduced in this paper in some cases can be applied directly to orbit matrices. In that way we obtain six new symmetric (64, 28, 12) designs. Further, we show that this type of switching (of trades) can be applied to any symmetric design related to a Bush-type Hadamard matrix and construct symmetric designs with parameters (36, 15, 6) leading to new Bush-type Hadamard matrices of order 36, and symmetric (100, 45, 20) designs yielding Bush-type Hadamard matrices of order 100. [ABSTRACT FROM AUTHOR]

Recent research has demonstrated a number of applications of the discrete Fourier transform to cyclic rhythms, addressing amongst other issues questions about conceptualizations of metre. One can apply a similar operation, the Hadamard transform, when the rhythmic cycle is a power of two. This paper explores some analytical applications of the Hadamard transform to repertoires where pure-duple metrical settings are the norm, such as American ragtime and Balinese gamelan. I compare it to the Fourier transform and highlight special features of the Hadamard transform of particular theoretical value, such as its sorting of rhythmic information into metrical levels, which leads to methods of classifying and quantifying syncopation. [ABSTRACT FROM AUTHOR]

In this work, we study the Hadamard-type k-step Pell sequence modulo m and then, we obtain the cyclic groups which are generated by the multiplicative orders of the Hadamard-type k-step Pell matrix when read modulo m. Then we extend the Hadamard-type k-step Pell sequence to groups and we redefine the Hadamard-type k-step Pell sequence by means of the elements of groups. Finally, we obtain the periods of the Hadamard-type 3- step Pell sequence in the semi-dihedral group SD2m and the quasidihedral group QD2m. [ABSTRACT FROM AUTHOR]

In this paper we establish existence results for a class of initial value problems for impulsive fractional differential equations involving the Caputo-Hadamard fractional derivative of order 1

In this paper, the concept of Gg-convex function is given the first time in the literature. Some inequalities of Hadamard's type for Gg-convex functions are given. Some algebraic properties of Gg-convex functions and special cases are discussed. In addition, we establish some new integral inequalities for Gg-convex functions by using an integral identity. [ABSTRACT FROM AUTHOR]

For positive invertible operators A on a Hilbert space H and a fixed unit vector x ∈ H, define the normalized determinant by ∆x(A):= exp hln Ax, xi. In this paper we obtain upper and lower bounds for the determinant ∆x (A ◦ B) of the Hadamard product of two operators under some natural assumptions such as 0 < m1 ≤ A ≤ M1 and 0 < m2 ≤ B ≤ M2, where mi, Mi (i = 1, 2) are constants. [ABSTRACT FROM AUTHOR]

In this paper, the properties of symbol transformations of cyclic Hadamard matrices are studied. An infinite class of (n − 1) -variable 2-resilient rotation symmetric Boolean functions are constructed, and the nonlinearity of the constructed functions is 2 n (n − 1). The crucial technique of this method is to determine a subset T ⊆ F 2 n − 1 satisfying a correspondent condition. This is a new construction of 2-resilient rotation symmetric Boolean functions via switching the supports of (n − 1) -variable rotation symmetric Boolean functions of degree one, i.e., f 0 n − 1 (x 1 , x 2 , ⋯ , x n − 1) = ⊕ i = 1 n − 1 x i , where n = 4 t. [ABSTRACT FROM AUTHOR]

This paper presents an efficient blind watermarking algorithm for double color images using Walsh Hadamard transform (WHT). In this algorithm, the energy gathering function of WHT and the strong correlation between the matrix coefficients in the frequency domain after transformation is used for embedding the digital watermark. Firstly, the color host image is divided into R, G, and B channels, and each channel is partitioned into 4 × 4 blocks. By researching the frequency domain coefficients of the WHT blocks, a strong correlation can be found between the coefficients of the first row of the frequency domain matrix, especially the first and second elements and the third and fourth elements in the first row. Therefore, the digital watermark can be embedded into the above matrix block by fine-tuning the mentioned coefficients, and the watermark information can be extracted by the difference between the two coefficients. According to a huge number of simulation results, the proposed algorithm shows better performance not only in invisibility but also in robustness, watermark capacity, and running time. [ABSTRACT FROM AUTHOR]

Digital image watermarking is the most widely used recognized approach to protect data against piracy. This paper proposes a new blind color image watermarking based on the Walsh Hadamard Transform (WHT). The proposed method subdivides the image into 4 × 4 non-overlapping blocks, which are then transformed using WHT. The color image watermark is embedded in the third and fourth-row WHT coefficients using the proposed technique as a slight change in those rows may not profoundly affect the visual quality of an image. Then the difference of the third and fourth row WHT coefficients of the watermarked image is obtained. The watermark information is extracted using the attained difference value. The performance evaluation of the proposed scheme outperforms in terms of embedding capacity, Peak Signal-to-Noise Ratio (PSNR), Weighted Peak Signal-to-Noise Ratio (WPSNR), Normalized cross-correlation (NC), and Structural Similarity Index (SSIM) than the conventional watermarking methods. This proposed method provides more robustness against several manipulations and lossy attacks. [ABSTRACT FROM AUTHOR]

Purpose: CSF plays important roles in clearing brain waste and homeostasis. However, mapping whole‐brain CSF flow in the rodents is difficult, primarily due to its assumed very low velocity. Therefore, we aimed to develop a novel phase‐contrast MRI method to map whole‐brain CSF flow in the mouse brain. Methods: A novel generalized Hadamard encoding–based multi‐band scheme (dubbed HEAP‐METRIC, Hadamard Encoding APproach of Multi‐band Excitation for short TR Imaging aCcelerating) using complex Hadamard matrix was developed and incorporated into conventional phase contrast (PC)‐MRI to significantly increase SNR. Results: Slow flow phantom imaging validated HEAP‐METRIC PC‐MRI's ability to achieve fast and accurate mapping of slow flow velocities (~102 µm/s). With the SNR gain afforded by HEAP‐METRIC scheme, high‐resolution (0.08 × 0.08 mm in‐plane resolution and 36 0.4 mm slices) PC‐MRI was completed in 21 min for whole‐brain CSF flow mapping in the mouse. Using this novel method, we provide the first report of whole‐brain CSF flow in the awake mouse brain with an average flow velocity of ~200 µm/s. Furthermore, HEAP‐METRIC PC‐MRI revealed CSF flow was reduced by isoflurane anesthesia, accompanied by reduction of glymphatic function as measured by dynamic contrast‐enhanced MRI. Conclusion: We developed and validated a generalized HEAP‐METRIC PC‐MRI for mapping low velocity flow. With this method, we have achieved the first whole‐brain mapping of awake mouse CSF flow and have further revealed that anesthesia reduces CSF flow velocity. [ABSTRACT FROM AUTHOR]

In recent studies of speech enhancement, a deep‐learning model is trained to predict clean speech spectra from the known noisy spectra of speech. Rather than using the traditional discrete Fourier transform (DFT), this paper considers other well‐known transforms to generate the speech spectra for deep‐learning‐based speech enhancement. In addition to the DFT, seven different transforms were tested: discrete Cosine transform, discrete Sine transform, discrete Haar transform, discrete Hadamard transform, discrete Tchebichef transform, discrete Krawtchouk transform, and discrete Tchebichef‐Krawtchouk transform. Two deep‐learning architectures were tested: convolutional neural networks (CNN) and fully connected neural networks. Experiments were performed for the NOIZEUS database, and various speech quality and intelligibility measures were adopted for performance evaluation. The quality and intelligibility scores of the enhanced speech demonstrate that discrete Sine transformation is better suited for the front‐end processing with a CNN as it outperformed the DFT in this kind of application. The achieved results demonstrate that combining two or more existing transforms could improve the performance in specific conditions. The tested models suggest that we should not assume that the DFT is optimal in front‐end processing with deep neural networks (DNNs). On this basis, other discrete transformations should be taken into account when designing robust DNN‐based speech processing applications. [ABSTRACT FROM AUTHOR]

The matrix S = [1+xiyj]i, j=1n, 0 < x1 < · · · < xn, 0 < y1 < · · · < yn, has gained importance lately due to its role in powers preserving total nonnegativity. We give an explicit decomposition of S in terms of elementary bidiagonal matrices, which is analogous to the Neville decomposition. We give a bidiagonal decomposition of S◦m = [(1+xiyj)m] for positive integers 1 ≤ m ≤ n-1. We also explore the total positivity of Hadamard powers of another important class of matrices called mean matrices. [ABSTRACT FROM AUTHOR]

In the field of skin disease diagnosis based on Convolutional Neural Networks (CNNs), there are currently two challenges. Firstly, there is a significant amount of label-independent information present in skin disease images. This information significantly affects the CNN's ability to recognize skin disease. Finding an effective way to remove this label-independence is a challenging problem. Secondly, most research focuses solely on information-limited RGB images. It is imperative to introduce additional color space views. Hence, there is a need to investigate which combinations of views are most effective for skin disease diagnosis. To address these two issues, this study first employs the information bottleneck theory to guide convolution operations, retaining relevant skin lesion information while filtering out irrelevant details. Secondly, through a view selection method, a combination of RGB, HSL, and YCbCr was chosen from seven views, which exhibited the best performance. A multi-view compression and collaboration (MCC) framework was constructed based on these two approaches. MCC assists CNNs in removing label-independent information while enriching image views, ultimately enhancing the diagnosis of skin diseases. To validate the effectiveness of MCC, experiments were conducted by using ResNet-50, DensNet-169, Inception-v4, and ConvNeXt-B on both a self-collected hyperpigmented skin disease dataset and a public ISIC2018 dataset. The experimental results show that MCC can effectively improve the accuracy, precision, recall, and F1-score of CNNs. Thus, MCC has the potential to assist medical professionals in more accurately diagnosing skin diseases in clinical practice, thereby improving healthcare services and patients' quality of life. • An effective and additive multi-view skin disease diagnosis model is proposed. • Redundant information perturbation and optimal view combination are considered. • Multi-view compression is proposed to alleviate redundant information disturbance. • Multi-view collaboration is proposed to flexibly choose the optimal view combination. • Several experiments verify the validity of the proposed model and its modules. [ABSTRACT FROM AUTHOR]

Modern experiments typically involve a very large number of variables. Screening designs allow experimenters to identify active factors in a minimum number of trials. To save costs, only low-level factorial designs are considered for screening experiments, especially two- and three-level designs. In this article, we provide a systematic method to construct screening designs that contain both two- and three-level factors based on Hadamard matrices with the fold-over structure. The proposed designs have good performance in terms of D-optimal and A-optimal criteria, and the estimates of the main effects are unbiased by the second-order effects, making them very suitable for screening experiments. Besides, some theoretical results on D- and A-optimality are obtained as a by-product. • The new method is easy to implement, utilizing Hadamard matrices and a fold-over structure. • The proposed designs have good performance in terms of D-optimal and A-optimal criteria. • The resulting designs ensure that the estimates of the main effects are unbiased for second-order effects. [ABSTRACT FROM AUTHOR]

In measuring a transmission matrix (TM) of a scattering medium, the normal way requires projecting a large number of patterns, resulting in significant measurement time. Here, we propose to do imaging through scattering media using a path-planning-based downsampling TM. The proposed method is verified by measuring TMs for imaging through scattering media when Walsh, Cake-cutting, and Russian doll Hadamard transforms (HTs) are adopted. Based on the spectral characteristics of different HTs of natural images, corresponding sampling paths are artificially planned, which guarantees the method to preferentially measure components in TM in relation to the more important spectra. This means that our method can reduce the number of patterns during measurement, thus improving the imaging speed while only sacrificing a little imaging quality. Experimental results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]