Harmonic wavelet transform

About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.

Directional hypercomplex wavelets for multidimensional signal analysis and processing

Abstract: We extend the wavelet transform to handle multidimensional signals that are smooth save for singularities along lower-dimensional manifolds. We first generalize the complex wavelet transform to higher dimensions using a multidimensional Hilbert transform. Then, using the resulting hypercomplex wavelet transform (HWT) as a building block, we construct new classes of nearly shift-invariant wavelet frames that are oriented along lower-dimensional subspaces. The HWT can be computed efficiently using a 1D dual-tree complex wavelet transform along each signal axis. We demonstrate how the HWT can be used for fast line detection in 3D.

Improved image watermarking scheme using fast Hadamard and discrete wavelet transforms

Abstract: We propose a robust image watermarking scheme by applying the fast Hadamard transform (FHT) to small blocks computed from the four discrete wavelet transform (DWT) subbands. Different transforms have different properties that can effectively match various aspects of the signal's frequencies. Our approach consists of four main steps: (1) we decomposed the original image into four subbands, (2) the four subbands are divided into blocks; (3) FHT is applied to each block; and (4) the singular-value decomposition (SVD) is applied to the watermark image prior to distributing the singular values over the DC components of the transformed blocks. The proposed technique improves the data embedding system effectively, the watermark imperceptibility, and its resistance to a wide range of intentional attacks. The experimental results demonstrate the improved performance of the proposed method in comparison with existing techniques in terms of the watermark imperceptibility and the robustness against attacks.

Direction-Adaptive Discrete Wavelet Transform via Directional Lifting and Bandeletization

Abstract: We propose an adaptive lifted discrete wavelet transform to locally adapt the filtering direction to the geometric flow in the image. The proposed approach refines previous directional lifting approaches to achieve superior compression performance with less demand for computation. Additionally, a bandeletization procedure is combined with directional lifting in a unified framework to further remove the correlation in the wavelet coefficients. Up to 2.8 dB improvement in PSNR over the conventional 2-D CDF 9/7 wavelet transform for natural images is reported. Significant improvement in subjective quality is also observed.

Compressive Video Sampling With Approximate Message Passing Decoding

Abstract: In this paper, we apply compressed sensing (CS) to video compression. CS techniques exploit the observation that one needs much fewer random measurements than given by the Shannon-Nyquist sampling theory to recover an object if this object is compressible (i.e., sparse in the spatial domain or in a transform domain). In the CS framework, we can achieve sensing, compression, and denoising simultaneously. We propose a fast and simple online encoding by the application of pseudorandom downsampling of the 2-D fast Fourier transform to video frames. For offline decoding, we apply a modification of the recently proposed approximate message passing (AMP) algorithm. The AMP method has been derived using the statistical concept of “state evolution,” and it has been shown to considerably accelerate the convergence rate in special CS-decoding applications. We shall prove that the AMP method can be rewritten as a forward-backward splitting algorithm. This new representation enables us to give conditions that ensure convergence of the AMP method and to modify the algorithm in order to achieve higher robustness. The success of reconstruction methods for video decoding also essentially depends on the chosen transform, where sparsity of the video signals is assumed. We propose incorporating the 3-D dual-tree complex wavelet transform that possesses sufficiently good directional selectivity while being computationally less expensive and less redundant than other directional 3-D wavelet transforms.

Identifying the Modal Parameters of a Structure from Ambient Vibration Data via the Stationary Wavelet Packet

Abstract: Ambient vibration tests are conducted widely to estimate the modal parameters of a structure. The work proposes an efficient wavelet-based approach to determine the modal parameters of a structure from its ambient vibration responses. The proposed approach integrates the time series autoregressive (AR) model with the stationary wavelet packet transform. In addition to providing a richer decomposition and allowing for an improved time–frequency localization of signals over that of the discrete wavelet transform, the stationary wavelet packet transform also has significantly higher computational efficiency than the wavelet packet transform in terms of decomposing time-shifted signals because the former has a time-invariance property. The correlation matrices needed in determining the coefficient matrices in an AR model are established in subspaces expanded by stationary wavelet packets. The formulation for estimating the correlation matrices is shown for the first time. Because different subspaces contain signals with different frequency subbands, the fine filtering property enhances the ability of the proposed approach to identify not only the modes with strong modal interference, but also many modes from the responses of very few measured degrees of freedom. The proposed approach is validated by processing the numerically simulated responses of a seven-floor shear building, which has closely spaced modes, with considering the effects of noise and incomplete measurements. Furthermore, the present approach is employed to process the velocity responses of an eight-storey steel frame subjected to white noise input in a shaking table test and ambient vibration responses of a cable-stayed bridge.