International Journal of Wavelets, Multiresolution and Information Processing

This paper investigates the scope of wavelets for performance improvement in spread spectrum image watermarking. Performance of a digital image watermarking algorithm, in general, is determined by the visual invisibility of the hidden data (imperceptibility), reliability in the detection of the hidden information after various common and deliberate signal processing operations (robustness) applied on the watermarked signals and the amount of data to be hidden (payload) without affecting the imperceptibility and robustness properties. In this paper, we propose a few spread spectrum (SS) image watermarking schemes using discrete wavelet transform (DWT), biorthogonal DWT and M-band wavelets coupled with various modulation, multiplexing and signaling techniques. The performance of the watermarking methods are also reported along with the relative merits and demerits.

Multiplicative cascades are often used to represent the structure of turbulence. Under the action of a multiplicative cascade, the relevant variables of the system can be understood as the result of a successive transfer of information in cascade from large to small scales. However, to make this cascade transfer explicit (i.e. being able to decompose each variable as the product of larger scale contributions) is only achieved when signals are represented in an optimal wavelet basis. Finding such a basis is a data-demanding, highly-complex task. In this paper, we propose a formalism that allows to find the optimal wavelet of a signal in an efficient, little data-demanding way. We confirm the appropriateness of this approach by analyzing the results on synthetic signals constructed with prescribed optimal bases. We show the validity of our approach constrained to given families of wavelets, though it can be generalized for a continuous unconstrained search scheme.

Recently, a new compressed-sensing (CS) theory for simultaneous sampling and compression of signals has been applied for imaging and remote sensing. The CS makes it possible for us to take super-resolution photos only using one or a few pixels rather than millions of pixels by conventional digital cameras. However, the performances of CS are related to choices of a measurement matrix and a sparse transform. In this paper, we present an experimentally comparing study for the use of different measurement matrices (e.g., random matrices, noiselet transform matrices, and scrambled block Hadamard ensemble) in encoding step and different geometric wavelets (e.g., curvelets and bandlets) in decoding step. Numerical experiments for single-pixel imaging and Fourier-domain multiple-pixel imaging indicate how to choose a suitable CS strategy to reduce the number of measurements and decoding costs.

Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows one to recover this signal from much fewer samples than the Shannon–Nyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms and others. Generally, wavelets represent point-like features while curvelets represent line-like features well. For a suitable recovery of images, we propose models that contain weighted sparsity constraints in two different frames. Given the incomplete measurements f = Φu + ϵ with the measurement matrix Φ ∈ ℝ^{K × N}, K ≪ N, we consider a jointly sparsity-constrained optimization problem of the form . Here Ψ_c and Ψ_w are the transform matrices corresponding to the two frames, and the diagonal matrices Λ_c, Λ_w contain the weights for the frame coefficients. We present efficient iteration methods to solve the optimization problem, based on Alternating Split Bregman algorithms. The convergence of the proposed iteration schemes will be proved by showing that they can be understood as special cases of the Douglas–Rachford Split algorithm. Numerical experiments for compressed sensing-based Fourier-domain random imaging show good performances of the proposed curvelet-wavelet regularized split Bregman (CWSpB) methods, where we particularly use a combination of wavelet and curvelet coefficients as sparsity constraints.

Taking advantage of both the scaling property of wavelets and the high learning ability of neural networks, wavelet networks have recently emerged as a powerful tool in many applications in the field of signal processing such as data compression, function approximation as well as image recognition and classification. A novel wavelet network-based method for image classification is presented in this paper. The method combines the Orthogonal Least Squares algorithm (OLS) with the Pyramidal Beta Wavelet Network architecture (PBWN). First, the structure of the Pyramidal Beta Wavelet Network is proposed and the OLS method is used to design it by presetting the widths of the hidden units in PBWN. Then, to enhance the performance of the obtained PBWN, a novel learning algorithm based on orthogonal least squares and frames theory is proposed, in which we use OLS to select the hidden nodes. In the simulation part, the proposed method is employed to classify colour images. Comparisons with some typical wavelet networks are presented and discussed. Simulations also show that the PBWN-orthogonal least squares (PBWN-OLS) algorithm, which combines PBWN with the OLS algorithm, results in better performance for colour image classification.

This paper deals with the wavelet-based performance analysis of the safety barrier for use in a full-scale test. The test involves a vehicle, a Ford Fiesta, which strikes the safety barrier at a prescribed angle and speed. The vehicle speed before the collision was measured. Vehicle accelerations in three directions at the center of gravity were measured during the collision. The yaw rate was measured with a gyro meter. Using normal speed and high-speed video cameras, the behavior of the safety barrier and the test vehicle during the collision was recorded. Based upon the results obtained, the tested safety barrier has proved to satisfy the requirements for an impact severity level. By taking into account the Haar wavelets, the property of integral operational matrix is utilized to find an algebraic representation form for calculate of wavelet coefficients of acceleration signals. It is shown that Haar wavelets can construct the acceleration signals well.

A Wilson orthonormal basis was constructed in 1991 by Daubechies, Jaffard and Journé from Gabor tight frame elements, when the redundancy of the Gabor system is 2. In 1994, Auscher gave a characterization of the atoms for which the Wilson system is an orthonormal basis. Afterwards, Gröchenig posed a question whether the construction of an orthonormal Wilson basis is possible for a Gabor tight frame of redundancy 3. We give a partial positive answer to this question constructing in this case a Wilson system being a tight frame with bound 1.

There should be different requirements for False Reject rate and False Accept rate in classification applications, and classifier learning should use an asymmetric factor to balance between False Reject rate and False Accept rate. A novel AdaBoost algorithm was developed with the asymmetric weight. Moreover we provide the theoretical analysis of its performance and derive the upper bound of the classification error.