Low Band Coefficients Research Articles

Computation of Wavelet and Multiwavelet Transforms Using Fast Fourier Transform

A novel fast and efficient algorithm was proposed that uses the Fast Fourier Transform (FFT) as a tool to compute the Discrete Wavelet Transform (DWT) and Discrete Multiwavelet Transform. The Haar Wavelet Transform and the GHM system are shown to be a special case of the proposed algorithm, where the discrete linear convolution will adapt to achieve the desired approximation and detail coefficients. Assuming that no intermediate coefficients are canceled and no approximations are made, the algorithm will give the exact solution. Hence the proposed algorithm provides an efficient complexity verses accuracy tradeoff. The main advantages of the proposed algorithm is that high band and the low band coefficients can be exploited for several classes of signals resulting in very low computation.

Fractional-pel Accurate Motion-Adaptive Transforms.

Fractional-pel accurate motion is widely used in video coding. For subband coding, fractional-pel accuracy is challenging since it is difficult to handle the complex motion field with temporal transforms. In our previous work, we designed integer accurate motion-adaptive transforms (MAT) which can transform integer accurate motion-connected coefficients. In this paper, we extend the integer MAT to fractional-pel accuracy. The integer MAT allows only one reference coefficient to be the lowband coefficient. In this paper, we design the transform such that it permits multiple references and generates multiple lowband coefficients. In addition, our fractional-pel MAT can incorporate a general interpolation filter into the basis vector, such that the highband coefficient produced by the transform is the same as the prediction error from the interpolation filter. The fractional-pel MAT is always orthonormal. Thus, the energy is preserved by the transform. We compare the proposed fractionalpel MAT, the integer MAT, and the half-pel motion-compensated orthogonal transform (MCOT), while HEVC intra coding is used to encode the temporal subbands. The experimental results show that the proposed fractional-pel MAT outperforms the integer MAT and the half-pel MCOT. The gain achieved by the proposed MAT over the integer MAT can reach up to 1dB in PSNR.

Poisson-Gaussian Noise Analysis and Estimation for Low-Dose X-ray Images in the NSCT Domain.

The noise distribution of images obtained by X-ray sensors in low-dosage situations can be analyzed using the Poisson and Gaussian mixture model. Multiscale conversion is one of the most popular noise reduction methods used in recent years. Estimation of the noise distribution of each subband in the multiscale domain is the most important factor in performing noise reduction, with non-subsampled contourlet transform (NSCT) representing an effective method for scale and direction decomposition. In this study, we use artificially generated noise to analyze and estimate the Poisson–Gaussian noise of low-dose X-ray images in the NSCT domain. The noise distribution of the subband coefficients is analyzed using the noiseless low-band coefficients and the variance of the noisy subband coefficients. The noise-after-transform also follows a Poisson–Gaussian distribution, and the relationship between the noise parameters of the subband and the full-band image is identified. We then analyze noise of actual images to validate the theoretical analysis. Comparison of the proposed noise estimation method with an existing noise reduction method confirms that the proposed method outperforms traditional methods.