Truncation Operation Research Articles

Application of Hilbert space operators on the sphere to directivity measurements

Spherical directivity measurements are useful for understanding and characterizing acoustic sources and are often applied to computer-based modeling and simulation of acoustic spaces. While the measurements must be handled with great care for suitable accuracy, little if any data post-processing has been employed in the past to ameliorate them and improve their utility. This paper outlines techniques utilizing Hilbert space operators on the unit sphere to both evaluate certain qualities of directivity measurements and provide refinements of their datasets. Truncation, projection, and symmetry operators on directivity measurements are specifically shown to benefit post-processing of the spherical functions.Spherical directivity measurements are useful for understanding and characterizing acoustic sources and are often applied to computer-based modeling and simulation of acoustic spaces. While the measurements must be handled with great care for suitable accuracy, little if any data post-processing has been employed in the past to ameliorate them and improve their utility. This paper outlines techniques utilizing Hilbert space operators on the unit sphere to both evaluate certain qualities of directivity measurements and provide refinements of their datasets. Truncation, projection, and symmetry operators on directivity measurements are specifically shown to benefit post-processing of the spherical functions.

Double JPEG Compression Detection Based on Noise-Free DCT Coefficients Mixture Histogram Model

With the wide use of various image altering tools, digital image manipulation becomes very convenient and easy, which makes the detection of image originality and authenticity significant. Among various image tampering detection tools, double JPEG image compression detector, which is not sensitive to specific image tampering operation, has received large attention. In this paper, we propose an improved double JPEG compression detection method based on noise-free DCT (Discrete Cosine Transform) coefficients mixture histogram model. Specifically, we first extract the block-wise DCT coefficients histogram and eliminate the quantization noise which introduced by rounding and truncation operations. Then, for each DCT frequency, a posterior probability can be obtained by solving the DCT coefficients mixture histogram with a simplified model. Finally, the probabilities from all the DCT frequencies are accumulated to give the posterior probability of a DCT block being authentic or tampered. Extensive experimental results in both quantitative and qualitative terms prove the superiority of our proposed method when compared with the state-of-the-art methods.

Data-driven internal multiple elimination and its consequences for imaging: A comparison of strategies

We have compared three data-driven internal multiple reflection elimination schemes derived from the Marchenko equations and inverse scattering series (ISS). The two schemes derived from Marchenko equations are similar but use different truncation operators. The first scheme creates a new data set without internal multiple reflections. The second scheme does the same and compensates for transmission losses in the primary reflections. The scheme derived from ISS is equal to the result after the first iteration of the first Marchenko-based scheme. It can attenuate internal multiple reflections with residuals. We evaluate the success of these schemes with 2D numerical examples. It is shown that Marchenko-based data-driven schemes are relatively more robust for internal multiple reflection elimination at a higher computational cost.

VOFTools 3.2: Added VOF functionality to initialize the liquid volume fraction in general convex cells

VOFTools 3.2: Added VOF functionality to initialize the liquid volume fraction in general convex cells

User-Friendly Covariance Estimation for Heavy-Tailed Distributions

We provide a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we introduce elementwise and spectrumwise truncation operators, as well as their $M$-estimator counterparts, to robustify the sample covariance matrix. Different from the classical notion of robustness that is characterized by the breakdown property, we focus on the tail robustness which is evidenced by the connection between nonasymptotic deviation and confidence level. The key insight is that estimators should adapt to the sample size, dimensionality and noise level to achieve optimal tradeoff between bias and robustness. Furthermore, to facilitate practical implementation, we propose data-driven procedures that automatically calibrate the tuning parameters. We demonstrate their applications to a series of structured models in high dimensions, including the bandable and low-rank covariance matrices and sparse precision matrices. Numerical studies lend strong support to the proposed methods.

On generalized principal eigenvalues of nonlocal operators witha drift

This article is concerned with the following spectral problem: to find a positive function φ∈C1(Ω) and λ∈R such that q(x)φ′(x)+∫ΩJ(x,y)φ(y)dy+a(x)φ(x)+λφ(x)=0forx∈Ω, where Ω⊂R is a non-empty domain (open interval), possibly unbounded, J is a positive continuous kernel, and a and q are continuous coefficients. Such a spectral problem naturally arises in the study of nonlocal population dynamics models defined in a space–time varying environment encoding the influence of a climate change through a spatial shift of the coefficient. In such models, working directly in a moving frame that matches the spatial shift leads to consider a problem where the dispersal of the population is modeled by a nonlocal operator with a drift term. Assuming that the drift q is a positive function, for rather general assumptions on J and a, we prove the existence of a principal eigenpair (λp,φp) and derive some of its main properties. In particular, we prove that λp(Ω)=limR→+∞λp(ΩR), where ΩR=Ω∩(−R,R) and λp(ΩR) corresponds to the principal eigenvalue of the truncation operator defined in ΩR. The proofs especially rely on the derivation of a new Harnack type inequality for positive solutions of such problems.

Fractional convolution and nonlinear operations applied to the image encryption

We use the fractional convolution, nonlinear operations and random phase masks (RPMs) in order to encrypt images. The definition used in this paper of the fractional convolution is based on the fractional Fourier transform (FrFT). The amplitude and phase truncation are nonlinear operations that allow to select a specific information of a complex-valued image. The encryption and decryption systems are based on the double random phase encoding (DRPE). At the beginning of the encryption process, the image to encrypt is encoded in phase. The rest of the encryption and decryption process use two RPMs, the fractional convolution and the amplitude and phase truncation operations in a sequential way in order to get the encrypted and decrypted image. The amplitude and phase truncation and the phase encoding are nonlinear operations that improving the security of the encrypted image, because the obtained key space of the proposed encryption process is very larger. The fractional order of the FrFT introduces a new key for the security system and the encrypted image of the proposed encryption system is a real-valued image. The encryption-decryption system has five security keys. All these five keys with their correct values are necessary in the decryption process with the purpose of obtaining the original image that was encrypted in the encryption process.

The optimal range of the Calderòn operator and its applications

We identify the optimal range of the Calderòn operator and that of the classical Hilbert transform in the class of symmetric quasi-Banach spaces. Further consequences of our approach concern the optimal range of the triangular truncation operator, operator Lipschitz functions and commutator estimates in ideals of compact operators.

An asymmetric multi-image cryptosystem based on cylindrical diffraction and phase truncation

An asymmetric multi-image cryptosystem is proposed by using the cylindrical diffraction and the phase truncation, which can avoid the vulnerability of the linear cryptosystems, simultaneously encrypt multiple images and decrypt images individually. In the proposed cryptosystem, four original images are modulated by four different random phases, respectively, and then their results are combined into one image by using convolution. The combined image is encoded into a real-value ciphertext by phase truncation after cylindrical diffraction, while the phase parts are saved as asymmetric decryption keys. Due to applications of the asymmetric cylindrical diffraction and the nonlinear operation of phase truncation, the cryptosystem can resist numerous types of attacks. The two main features of the proposed cryptosystem are to encrypt multi-image without time increasing linearly and individually decrypt multi-image with highly flexible. The security and flexibility of the proposed cryptosystem are demonstrated by numerical simulation results.

Scalable asymmetric image encryption based on phase-truncation in cylindrical diffraction domain

In this paper, a scalable asymmetric image compression and encryption method is proposed based on discrete wavelet transform (DWT) and nonlinear operations in the cylindrical diffraction domain. In this scheme, the grayscale image is processed by a DWT, and four component images are obtained. Then single amplitude ciphertext is obtained by nonlinear operation of phase truncation after cylindrical diffraction. Since the reconstruction from the four component images of DWT is scalable, the proposed method also has scalability. Moreover, the proposed method has high security because it can resist the phase-retrieval attack and prevent information disclosure. Numerical simulations have demonstrated the security and effectiveness of the proposed method.

Non-convex analytical and geometrical tools for volume truncation, initialization and conservation enforcement in VOF methods

A set of non-convex calculation tools for volume of fluid (VOF) methods in general grids is presented. The complexity of the volume truncation operation and the computation of the interface position to cut off a certain liquid volume fraction from a cell, involved in VOF methods, is greatly increased when non-convex grids and polytopes are considered. Therefore, the tools for convex geometries developed in a previous work by López and Hernández (2008) [32] have required profound adaptation for the different algorithms not only to address the challenges of the new geometry, but also to maintain the efficiency and robustness of previous tools. Also, a new method for the liquid volume initialization in general polygonal and polyhedral cells, either convex or non-convex, is proposed. A comparison with conventional procedures based on convex decomposition is carried out using different tests, whereby it is demonstrated that the proposed tools represent a substantial improvement in computational efficiency. Overall, a speedup of around one order of magnitude is achieved for the reconstruction of several 2D and 3D interfacial shapes.

Nonlinear encryption system based on the fractional Fourier operators and truncation operations

In this paper, the fractional Fourier operators, the random phase masks and the nonlinear operations of amplitude and phase truncations are utilized to encrypt and decrypt images. We use the following fractional Fourier operators in the image encryption-decryption system: the fractional Fourier transform, the fractional traslation and the fractional correlation. The proposed encryption system uses nonlinear operations, such as phase encoding and truncation operations, in order to increase the security of the encrypted image. The encryption-decryption system has the following security keys: one fractional order of the fractional Fourier transform, two random phase masks and two pseudorandom code images. When all the proper security keys are used in the decryption system, the obtained decrypted image is a replica of the image to encrypt.

Two Weight Characterization of New Maximal Operators

For the last twenty years, there has been a great deal of interest in the theory of two weight. In the present paper, we investigate the two weight norm inequalities for fractional new maximal operator on the Lebesgue space. More specifically, we obtain that the sufficient and necessary conditions for strong and weak type two weight norm inequalities for a new fractional maximal operators by introducing a class of new two weight functions. In the discussion of strong type two weight norm inequalities, we make full use of the properties of dyadic cubes and truncation operators, and utilize the space decomposition technique which space is decomposed into disjoint unions. In contrast, weak type two weight norm inequalities are more complex. We have the aid of some good properties of <i>A_p</i> weight functions and ingeniously use the characteristic function. What should be stressed is that the new two weight functions we introduced contains the classical two weights and our results generalize known results before. In this paper, it is worth noting that <i>w</i>(x)<i>dx</i> may not be a doubling measure if our new weight functions <i>ω∈Ap (φ)</i>. Since <i>φ(|Q|)≥1</i>, our new weight functions are including the classical Muckenhoupt weights.

Asymmetric encryption of multiple-image based on compressed sensing and phase-truncation in cylindrical diffraction domain

In this paper, an asymmetric multiple-image encryption algorithm based on compressed sensing and cylindrical diffraction is proposed. Firstly, these multiple gray scale images are compressed by compressed sensing in separately. Then single amplitude ciphertext is obtained by asymmetric operation of phase truncation after cylindrical diffraction. This method not only can achieve multiple-image encryption with a small amount of data, but also can prevent information disclosure. Moreover, the proposed method has high security because it can resist the phase-retrieval attack. Numerical simulations have demonstrated the security and effectiveness of the proposed method.

Artifact-free reverse time migration

We have derived an improved reverse time migration (RTM) scheme to image the medium without artifacts arising from internal multiple reflections. This is based on a revised implementation of Marchenko redatuming using a new time-truncation operator. Because of the new truncation operator, we can use the time-reversed version of the standard wavefield-extrapolation operator as initial estimate for retrieving the upgoing focusing function. Then, the retrieved upgoing focusing function can be used to directly image the medium by correlating it with the standard wavefield-extrapolation operator. This imaging scheme can be seen as an artifact-free RTM scheme with two terms. The first term gives the conventional RTM image with the wrong amplitude and artifacts due to internal multiple reflections. The second term gives a correction image that can be used to correct the amplitude and remove artifacts in the image generated by the first term. We evaluated the success of the method with a 2D numerical example.

Understanding the Hawthorne effect in wound research-A scoping review.

The Hawthorne Effect (HE) is considered a methodological artefact in research, although its definition and influence on research outcomes lack consensus. This review explored how this term has been mentioned and discussed in the area of wound research. A scoping review was conducted on ProQuest Central, Scopus, EbscoHost, and online databases of indexed wound journals using the methodological framework by Arksey and Malley. A review protocol was applied to detail key terms, truncation and Boolean operators, and inclusion and exclusion criteria. Search findings were reported using PRISMA guidelines. A total of 38 articles reporting primary evidence were identified. Three themes emerged from the review: wound researchers' awareness of HE, the acknowledgement of the existence or otherwise of HE, and the mentioning of HE in passing. These results reflect a lack of attention to and understanding and awareness of the HE in the area of wound research. It is suggested that the HE receives more attention as a methodological concern, and its potential influence is considered and mitigated when planning future studies. Recommendations are provided to minimise the impact of the HE on the rigour of the research and confidence afforded to research findings.

Iterative learning scheme‐based fault estimation design for nonlinear systems with varying trial lengths and specified constraints

SummaryThis technical note deals with a fault estimation (FE) problem for nonlinear systems with varying trial lengths subjected to specified constraints. An iterative learning observer is developed to achieve FE and state reconstruction simultaneously, which thus to consider the state error and fault estimating information from previous iteration to improve the FE performance in the current iteration. Compared with conventional observer‐based FE methods, the proposed method only requires the bounds of parameter matrices rather than the precise model of the system. To deal with the missing and redundancy problems caused by varying trial lengths, a truncation operator is presented to design the FE law. Different from existing iterative learning methods, the presented method aims at the nonlinear systems with specified constraints, such as filling systems. Furthermore, the λ‐norm method and mathematical induction are employed to obtain the solutions of iterative learning matrices and observer gain matrix. Finally, illustrative examples are introduced to demonstrate the validity and the effectiveness of the proposed FE approach.

Simple hash function using discrete-time quantum walks

Hash functions play an essential role in many cryptographic applications such as digital signature, integrity authentication, and key derivation. Most of them are iteratively built based on the Merkle–Damgard (MD) structure. Unfortunately the traditional MD structure is suffering from various attacks, and thus the design of new hash functions is emerging. In this paper, inspired by quantum computation, we present a new hash function by introducing alternate single-qubit coin operators into discrete-time quantum walk. The present hash function is classical with classical input and output. The compressive function can be implemented by performing alternate single-qubit coin operators on the coin state controlled by a classical input binary message and then applying the global conditional shift operator on the position state and the coin state. The classical output hash value is generated by making amplification, truncation, and modular operation on the final probability distribution. Numerical simulation and performance comparison show that the present hash function has an excellent property of collision resistance and easier implementation than existing quantum-walk-based hash functions. It promotes more applications of quantum computation in the design of hash functions.

Nonlinear double image encryption using 2D non-separable linear canonical transform and phase retrieval algorithm

In this paper, we propose a new asymmetric method for double image encryption using the two-dimensional non-separable linear canonical transform (2D NS-LCT) and an iterative phase retrieval algorithm (PRA). First an encryption security key is generated using the PRA. Then two images (2D intensities) are combined to form a complex image. The 2D NS-LCT of this complex valued image is then obtained. A nonlinear phase truncation operation is applied to the transformed image and the amplitude is retained and used as the private key. The phase term is multiplied by the security PRA generated key and the inverse 2D NS-LCT is applied to the result giving the output encrypted image. The robustness of the proposed technique is tested against noise, occlusion and chosen-plaintext attacks. Numerical results are presented demonstrating the security of the proposed technique.

IIR Filter Architectures with Truncation Error Feedback for ECG Signal Processing

This work proposes fixed-point hardware architectures for two IIR filters, focusing on design specifications for ECG signal processing, using the truncation error feedback (TEF) to attenuate errors caused by truncation operations inside these recursive structures. The TEF is represented by modulo operation followed by a unit-delay operator and multiplication by a coefficient. In this work, the proposed TEF core consists of a hardware structure based on delay, right-shift and modulo operations. The TEF approach is applied to sequential and parallel IIR filter architectures with fixed and adaptive coefficients. The first structure comprises a first-order high-pass filter applied to attenuate low frequencies of the electrocardiogram (ECG) signal. The second one is a second-order infinite impulse response (IIR) adaptive notch filter used to attenuate power line interference signals. All dedicated architectures were described and simulated using VHDL and synthesized in Cadence environment using the 45 nm Nangate Open Cell Library to verify the results of the area, delay and power metrics. A simulated ECG signal was used as input to check the functionality of the filters. Our results indicate that the TEF approach was useful for both high-pass filter (HPF) and adaptive notch filter (ANF), and it can be a significant strategy to meet design specifications and dynamic performance of fixed-point digital filters. For the synthesis analysis, both HPF and ANF sequential filters had lower power and cell area figures but presented higher normalized power per sample and delay. In summation, the TEF approach enabled the use of fixed-point filters for ECG filtering without degrading their dynamic performance or increasing noise caused by truncation.