Discrete sine transform

About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.

Factorization of the coefficient variance matrix in orthogonal transforms

Abstract: The authors derive a matrix factorization of the coefficient variances for any fixed transformation. This factorization formulation provides a better framework for understanding the role of transform on the one hand, and the signal source model on the other. It also greatly simplifies the number of computational operations required for each variance calculation. A transform-specific matrix which links the transform to the signal correlation model is derived. This factorization provides a conceptual framework for understanding the behaviour of the transform for different source models. It also significantly simplifies the calculation of the variance of each transform coefficient from a quadruple sum over four indices to a double sum over two indices. This simplification can be used in adaptive transform coding which requires an estimate of the variances. Test results demonstrate that this mode-based variance calculation provides an accurate basis for adaptive transform coding, particularly at low bit rates. >

Spectral analysis of cervical cells using the discrete Fourier transform.

Abstract: This paper contains results from a preliminary study of spectral analysis techniques applied to the classification of cervical cells from routinely prepared Papanicolaou cervical smears. Experiments were conducted using a subset of 110 normals and 110 dyskaryotic single cell images randomly selected from a larger cell image data base. An assessment was made of the contribution of different regions within a cell image to the frequency spectrum. Three image sets were used, the original image itself plus two derived from it. In the first derived set, only nuclear size and shape were used. In the second set nuclear morphology and texture were included. Nuclear masking was performed using an interactive segmentation procedure. The discrete Fourier transform was applied to each image in the three image sets and classification experiments were performed using 80 features derived from the frequency spectra. An optimum set of features was selected for each experiment by canonical analysis. Good classification results were obtained when features extracted solely from nuclear shape were used. The inclusion of information relating to nuclear texture improved the results. However, inclusion of the extra nuclear region degraded the classifier's ability to discriminate between cell groups.

A Fast Algorithm for Solving the Space-Time Fractional Diffusion Equation

Abstract: In this paper, we propose a fast algorithm for efficient and accurate solution of the space–time fractional diffusion equations defined in a rectangular domain. The spatial discretization is done by using the central finite difference scheme and matrix transfer technique. Due to its nonlocality, numerical discretization of the spectral fractional Laplacian ( − Δ ) s α / 2 results in a large dense matrix. This causes considerable challenges not only for storing the matrix but also for computing matrix–vector products in practice. By utilizing the compact structure of the discrete system and the discrete sine transform, our algorithm avoids to store the large matrix from discretizing the nonlocal operator and also significantly reduces the computational costs. We then use the Laplace transform method for time integration of the semi-discretized system and a weighted trapezoidal method to numerically compute the convolutions needed in the resulting scheme. Various experiments are presented to demonstrate the efficiency and accuracy of our method.