Showing papers on "Hadamard transform published in 2008"

ON SOME HADAMARD-TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS

Abstract: In this paper, some inequalities Hadamard-type for h-convex functions are given. We also proved some Hadamard-type inequalities for products of two h-convex functions.

Fast compressive imaging using scrambled block Hadamard ensemble

Abstract: With the advent of a single-pixel camera, compressive imaging applications have gained wide interests. However, the design of efficient measurement basis in such a system remains as a challenging problem. In this paper, we propose a highly sparse and fast sampling operator based on the scrambled block Hadamard ensemble. Despite its simplicity, the proposed measurement operator offers universality and requires a near-optimal number of samples for perfect reconstruction. Moreover, it can be easily implemented in the optical domain thanks to its integer-valued elements. Several numerical experiments show that its imaging performance is comparable to that of the dense, floating-coefficient scrambled Fourier ensemble at much lower implementation cost.

Hadamard-Type Inequalities for s-Convex Functions

Abstract: In this paper a Hadamard’s type inequalities for s–convex functions in both sense and s–convex functions on the co–ordinates are given

Hadamard, Khatri-Rao, Kronecker and Other Matrix Products

Abstract: In this paper we present a brief overview on Hadamard, KhatriRao, Kronecker and several related non-simple matrix products and their properties. We include practical applications, in different areas, of some of the al-

Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension

Abstract: We develop the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension. Our formalism could be helpful in treating some aspects of the quantum physics of extra spatial dimensions. More precisely, for spacetime dimensions up to six, we explicitly describe the Hadamard renormalization procedure and for spacetime dimensions from 7 to 11, we provide the framework permitting the interested reader to perform this procedure explicitly in a given spacetime. We complete our study (i) by considering the ambiguities of the Hadamard renormalization of the stress-energy tensor and the corresponding ambiguities for the trace anomaly, (ii) by providing the expressions of the gravitational counterterms involved in the renormalization process, and (iii) by discussing the connections between Hadamard renormalization and renormalization in the effective action. All our results are expanded on standard bases for Riemann polynomials constructed from group theoretical considerations and thus given on irreducible forms.

Hadamard type inequalities for m-convex and (alpha, m)-convex functions

Abstract: In this paper we establish several Hadamard type inequalities for differentiable m-convex and (α , m)-convex functions. We also establish Hadamard type inequalities for products of two m-convex or (α , m)-convex functions. Our results generalize some results of B.G. Pachpatte as well as some results of C.E.M. Pearce and J. Pecaric.

Spectral Logic and Its Applications for the Design of Digital Devices

Abstract: PREFACE. ACKNOWLEDGMENTS. LIST OF FIGURES. LIST OF TABLES. ACRONYMS.1. LOGIC FUNCTIONS. 1.1 Discrete Functions. 1.2 Tabular Representations of Discrete Functions. 1.3 Functional Expressions. 1.4 Decision Diagrams for Discrete Functions. 1.5 Spectral Representations of Logic Functions. 1.6 Fixed-polarity Reed-Muller Expressions of Logic.Functions. 1.7 Kronecker Expressions of Logic Functions. 1.8 Circuit Implementation of Logic Functions. 2. SPECTRAL TRANSFORMS FOR LOGIC FUNCTIONS. 2.1 Algebraic Structures for Spectral Transforms. 2.2 Fourier Series. 2.3 Bases for Systems of Boolean Functions. 2.4 Walsh Related Transforms. 2.5 Bases for Systems of Multiple-Valued Functions. 2.6 Properties of DiscreteWalsh andVilenkin-Chrestenson Transforms. 2.7 Autocorrelation and Cross-Correlation Functions. 2.8 Harmonic Analysis over an Arbitrary Finite Abelian Group. 2.9 Fourier Transform on Finite Non-Abelian Groups. 3. CALCULATION OF SPECTRAL TRANSFORMS. 3.1 Calculation of Walsh Spectra. 3.2 Calculation of the Haar Spectrum. 3.3 Calculation of the Vilenkin-Chrestenson Spectrum. 3.4 Calculation of the Generalized Haar Spectrum. 3.5 Calculation of Autocorrelation Functions. 4. SPECTRAL METHODS IN OPTIMIZATION OF DECISION DIAGRAMS. 4.1 Reduction of Sizes of Decision Diagrams. 4.2 Construction of Linearly Transformed Binary Decision Diagrams. 4.3 Construction of Linearly Transformed Planar BDD. 4.4 Spectral Interpretation of Decision Diagrams. 5. ANALYSIS AND OPTIMIZATION OF LOGIC FUNCTIONS. 5.1 Spectral Analysis of Boolean Functions. 5.2 Analysis and Synthesis of Threshold Element Networks. 5.3 Complexity of Logic Functions. 5.4 Serial Decomposition of Systems of Switching Functions. 5.5 Parallel Decomposition of Systems of Switching Functions. 6. SPECTRAL METHODS IN SYNTHESIS OF LOGIC NETWORKS. 6.1 Spectral Methods of Synthesis of Combinatorial Devices. 6.2 Spectral Methods for Synthesis of Incompletely Specified Functions. 6.3 Spectral Methods of Synthesis of Multiple-Valued Functions. 6.4 Spectral Synthesis of Digital Functions and Sequences Generators. 7. SPECTRAL METHODS OF SYNTHESIS OF SEQUENTIAL MACHINES. 7.1 Realization of Finite Automata by Spectral Methods. 7.2 Assignment of States and Inputs for Completely Specified Automata. 7.3 State Assignment for Incompletely Specified Automata. 7.4 Some Special Cases of the Assignment Problem. 8. HARDWARE IMPLEMENTATION OF SPECTRAL METHODS. 8.1 Spectral Methods of Synthesis with ROM. 8.2 Serial Implementation of Spectral Methods. 8.3 Sequential Haar Networks. 8.4 Complexity of Serial Realization by Haar Series. 8.5 Parallel Realization of Spectral Methods of Synthesis. 8.6 Complexity of Parallel Realization. 8.7 Realization by Expansions over Finite Fields. 9. SPECTRAL METHODS OF ANALYSIS AND SYNTHESIS OF RELIABLE DEVICES. 9.1 Spectral Methods for Analysis of Error Correcting Capabilities. 9.2 Spectral Methods for Synthesis of Reliable Digital Devices. 9.3 Correcting Capability of Sequential Machines. 9.4 Synthesis of Fault-Tolerant Automata with Self-Error Correction. 9.5 Comparison of Spectral and Classical Methods. 10. SPECTRAL METHODS FOR TESTING OF DIGITAL SYSTEMS. 10.1 Testing and Diagnosis by Verification of Walsh Coefficients. 10.2 Functional Testing, Error Detection, and Correction by Linear Checks. 10.3 Linear Checks for Processors. 10.4 Linear Checks for Error Detection in Polynomial Computations. 10.5 Construction of Optimal Linear Checks for Polynomial Computations. 10.6 Implementations and Error-Detecting Capabilities of Linear Checks. 10.7 Testing for Numerical Computations. 10.8 Optimal Inequality Checks and Error-Correcting Codes. 10.9 Error Detection in Computer Memories by Linear Checks. 10.10 Location of Errors in ROMs by Two Orthogonal Inequality Checks. 10.11 Detection and Location of Errors in Random-Access Memories. 11. EXAMPLES OF APPLICATIONS AND GENERALIZATIONS OF SPECTRAL METHODS ON LOGIC FUNCTIONS. 11.1 Transforms Designed for Particular Applications. 11.2 Wavelet Transforms. 11.3 Fibonacci Transforms. 11.4 Two-Dimensional Spectral Transforms. 11.5 Application of the Walsh Transform in Broadband Radio. APPENDIX A. REFERENCES. INDEX.

Three factor scheme for biometric-based cryptographic key regeneration using iris

Abstract: In this paper we propose a three factor (smart card, iris code and password) scheme for cryptographic key regeneration based on fuzzy sketches idea which handles biometric variability with error correcting codes. Because errors in iris codes have mixed nature (random and burst errors), concatenated Hadamard and Reed-Solomon codes are used in this work. Hadamard codes can correct up to 25% errors but experiments showed that it is necessary to increase this capacity. In order to correct this higher amount of errors, a zero padding scheme is introduced. In addition, a user specific iris code shuffling key is used which increases the separation between genuine and impostor Hamming distance distributions, providing better separability between genuine users and impostors. We succeeded in regenerating a 198-bit key with estimated entropy of 83 bits on the NIST-ICE database at 0.055% False Acceptance Rate (FAR) and 1.04% False Rejection Rate (FRR).

HADAMARD TYPE INEQUALITIES FORm-CONVEX AND (,m )-CONVEX FUNCTIONS

Abstract: In this paper we establish several Hadamard type inequalities for differentiable m- convex and (,m )-convex functions. We also establish Hadamard type inequalities for products of two m-convex or (,m )-convex functions. Our results generalize some results of B.G. Pach- patte as well as some results of C.E.M. Pearce and J. Peˇ cari´ c.

Local Convergence of the Proximal Point Method for a Special Class of Nonconvex Functions on Hadamard Manifolds

Abstract: Local convergence analysis of the proximal point method for special class of nonconvex function on Hadamard manifold is presented in this paper. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, is proved that each cluster point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minimizer is obtained.

Sequency-Ordered Complex Hadamard Transform: Properties, Computational Complexity and Applications

Abstract: In this paper, the generation of sequency-ordered complex Hadamard transform (SCHT) based on the complex Rademacher matrices is presented. The exponential form of SCHT is also derived, and the proof for the unitary property of SCHT is given. Using the sparse matrix factorization, the fast and efficient algorithm to compute the SCHT transform is developed, and its computation load is described. Certain properties of the SCHT matrices are derived and analyzed with the discussion of SCHT applications in spectrum analysis and image watermarking. Relations of SCHT with fast Fourier transform (FFT) and unified complex Hadamard transform (UCHT) are discussed.

The superconvergence of Newton–Cotes rules for the Hadamard finite-part integral on an interval

Abstract: We study the general (composite) Newton–Cotes rules for the computation of Hadamard finite-part integral with the second-order singularity and focus on their pointwise superconvergence phenomenon, i.e., when the singular point coincides with some a priori known point, the convergence rate is higher than what is globally possible. We show that the superconvergence rate of the (composite) Newton–Cotes rules occurs at the zeros of a special function and prove the existence of the superconvergence points. Several numerical examples are provided to validate the theoretical analysis.

A low complexity and lossless frame memory compression for display devices

Abstract: In this paper, we introduce a new low complexity and lossless algorithm based on subband decomposition with the modified Hadamard transform (MHT) and adaptive Golomb-Rice (AGR) coding for display devices. The main goal of the proposed method is to reduce memory requirement for display devices. A basic unit of the proposed method is a line of the image so that the method is processed line by line. Also, MHT and AGR coding are utilized to achieve low complexity. The major improvement of the method is from the use of AGR and subband processing compared with exiting methods which are similar to the method in terms of complexity and applications. Simulation results show that the algorithm achieves a superior compression performance to the existing methods. In addition, the proposed method is hardware-friendly and could be easily implemented in any display devices.

Spectral amplitude coding OCDMA using and subtraction technique.

Abstract: An optical decoding technique is proposed for a spectral-amplitude-coding-optical code division multiple access, namely, the AND subtraction technique. The theory is being elaborated and experimental results have been done by comparing a double-weight code against the existing code, Hadamard. We have proved that the and subtraction technique gives better bit error rate performance than the conventional complementary subtraction technique against the received power level.

Co-ordinated s-Convex Function in the First Sense with Some Hadamard-Type Inequalities

Abstract: In this paper a Hadamard’s type inequality of s–convex function in first sense and s–convex function of 2–variables on the co–ordinates are given. A monotonic nondecreasing mapping connected with the Hadamard’s inequality for Lipschitzian s–convex mapping in the first sense of one variable is established.

The Hadamard's Inequality for s-Convex Function

Abstract: A monotone nondecreasing mapping connected with Hadamard– type inequality for s–convex function and some applications are given.

Proximal Point Method for a Special Class of Nonconvex Functions on Hadamard Manifolds

Abstract: In this paper we present the proximal point method for a special class of nonconvex function on a Hadamard manifold. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, it is proved that each accumulation point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minimizer is obtained.

A Generalized Reverse Block Jacket Transform

Abstract: Jacket matrices motivated by the center weight Hadamard matrices have played important roles in signal processing, communication, image compression, cryptography, etc. In this paper we propose a notation called block Jacket matrix which substitutes elements of the matrix into common matrices or even block matrices. Employing the well-known Pauli matrices which are very important in many subjects, block Jacket matrices with any size are investigated in detail, and some recursive relations for fast construction of the block Jacket matrices are obtained. Based on the general recursive relations, several special block Jacket matrices are constructed. To decompose high order block Jacket matrices, a fast decomposition algorithm for the factorable block Jacket matrices is suggested. After that some properties of the block Jacket matrices are investigated. Finally, several remarks are presented. These remarks are associated with comparisons between the Clifford algebra and the block Jacket matrices, generations of orthogonal and quasi-orthogonal sequences, and relations of the block Jacket matrices to the orthogonal transforms for signal processing. Since the Pauli matrices are actually infinitesimal generators of SU(2) group, the proposed construction and decomposition algorithms for the block Jacket matrices are available in the signal processing, communication, quantum signal processing and information theory.

Parametrizing complex Hadamard matrices

Abstract: The purpose of this paper is to introduce new parametric families of complex Hadamard matrices in two different ways. First, we prove that every real Hadamard matrix of order N>=4 admits an affine orbit. This settles a recent open problem of Tadej and Zyczkowski [W. Tadej, K. Zyczkowski, A concise guide to complex Hadamard matrices, Open Syst. Inf. Dyn. 13 (2006) 133-177], who asked whether a real Hadamard matrix can be isolated among complex ones. In particular, we apply our construction to the only (up to equivalence) real Hadamard matrix of order 12 and show that the arising affine family is different from all previously known examples listed in [W. Tadej, K. Zyczkowski, A concise guide to complex Hadamard matrices, Open Syst. Inf. Dyn. 13 (2006) 133-177]. Second, we recall a well-known construction related to real conference matrices, and show how to introduce an affine parameter in the arising complex Hadamard matrices. This leads to new parametric families of orders 10 and 14. An interesting feature of both of our constructions is that the arising families cannot be obtained via Dita's general method [P. Dita, Some results on the parametrization of complex Hadamard matrices, J. Phys. A 37 (20) (2004) 5355-5374]. Our results extend the recent catalogue of complex Hadamard matrices [W. Tadej, K. Zyczkowski, A concise guide to complex Hadamard matrices, Open Syst. Inf. Dyn. 13 (2006) 133-177], and may lead to direct applications in quantum-information theory.

Towards a Classification of 6 × 6 Complex Hadamard Matrices

Abstract: Complex Hadamard matrices have received considerable attention in the past few years due to their application in quantum information theory. While a complete characterization currently available [5] is only up to order 5, several new constructions of higher order matrices have appeared recently [4, 12, 2, 7, 11]. In particular, the classification of self-adjoint complex Hadamard matrices of order 6 was completed by Beuachamp and Nicoara in [2], providing a previously unknown non-affine one-parameter orbit. In this paper we classify all dephased, symmetric complex Hadamard matrices with real diagonal of order 6. Furthermore, relaxing the condition on the diagonal entries we obtain a new non-affine one-parameter orbit connecting the Fourier matrix F6 and Diţa's matrix D6. This answers a recent question of Bengtsson et al. [3].

New Design of Quaternary Low-Correlation Zone Sequence Sets and Quaternary Hadamard Matrices

Abstract: In this correspondence, we present new construction methods for quaternary low-correlation zone (LCZ) sequence sets from a binary sequence with good autocorrelation. We show that the sets obtained by our methods are optimal or nearly optimal with respect to the Tang-Fan-Matsufuji bound and that our construction methods are more flexible than any other previous constructions in the sense of period, family size, and zone size. We also give a construction method for a quaternary LCZ sequence set from a binary LCZ sequence set. Finally, we give a new construction method for quaternary Hadamard matrices by the inverse of the Gray map.

Motion Feature and Hadamard Coefficient-Based Fast Multiple Reference Frame Motion Estimation for H.264

Abstract: In the state-of-the-art video coding standard, H.264/AVC, the encoder is allowed to search for its prediction signals among a large number of reference pictures that have been decoded and stored in the decoder to enhance its coding efficiency. Therefore, the computation complexity of the motion estimation (ME) increases linearly with the number of reference picture. Many fast multiple reference frame ME algorithms have been proposed, whose performance, however, will be considerably degraded in the hardwired encoder design due to the macroblock (MB) pipelining architecture. Considering the limitations of the traditional four-stage MB pipelining architecture, two fast multiple reference frame ME algorithms are proposed here. First, on the basis of mathematical analysis, which reveals that the efficiency of multiple reference frames will be degraded by the relative motion between the camera and the objects, for the slow-moving MB, the authors adopt the multiple reference frames but reduce their search range. On the other hand, for the fast-moving MB, the first previous reference frame is used with the full search range during the ME processing. The mutually exclusive feature between the large search range and the multiple reference frames makes the computation saving performance of the proposed algorithm insensitive to the nature of video sequence. Second, following the Hadamard transform coefficient-based all_zeros block early detection algorithm, two early termination criteria are proposed. These methods ensure the pronounced computation saving efficiency when the encoded video has strong spatial homogeneity or temporal stationarity. Experimental results show that 72.7%-93.7% computation can be saved by the proposed fast algorithms with an average of 0.0899 dB coding quality degradation. Moreover, these fast algorithms can be combined with fast block matching algorithms to further improve their speedup performance.

Generalized Commuting Matrices and Their Eigenvectors for DFTs, Offset DFTs, and Other Periodic Operations

Abstract: It is well known that some matrices (such as Dickinson-Steiglitz's matrix) can commute with the discrete Fourier transform (DFT) and that one can use them to derive the complete and orthogonal DFT eigenvector set. Recently, Candan found the general form of the DFT commuting matrix. In this paper, we further extend the previous work and find the general form of the commuting matrix for any periodic, quasi-periodic, and offset quasi-periodic operations. Using the general commuting matrix, we can derive the complete and orthogonal eigenvector sets for offset DFTs, DCTs of types 1, 4, 5, and 8, DSTs of types 1, 4, 5, and 8, discrete Hartley transforms of types 1 and 4, the Walsh transform, and the projection operation (the operation that maps a whole vector space into a subspace) successfully. Moreover, several novel ways of finding DFT eigenfunctions are also proposed. Furthermore, we also extend our theories to the continuous case, i.e., if a continuous transform is periodic, quasi-periodic, or offset quasi-periodic (such as the FT and some cyclic operations in optics), we can find the general form of the commuting operation and then find the complete and orthogonal eigenfunctions set for the continuous transform.

Switching Operations for Hadamard Matrices

Abstract: We define several operations that switch substructures of Hadamard matrices, thereby producing new, generally inequivalent, Hadamard matrices. These operations have application to the enumeration and classification of Hadamard matrices. To illustrate their power, we use them to greatly improve the lower bounds on the number of equivalence classes of Hadamard matrices in orders 32 and 36 to 3,578,006 and 18,292,717.