Seisuke Kyochi

General Factorization of Conjugate-Symmetric Hadamard Transforms

Complex-valued conjugate-symmetric Hadamard transforms (C-CSHT) are variants of complex Hadamard transforms and found applications in signal processing. In addition, their real-valued transform counterparts (R-CSHTs) perform comparably with Hadamard transforms (HTs) despite their lower computational complexity. Closed-form factorizations of C-CSHTs and R-CSHTs have recently been proposed to make calculations more efficient. However, there is still room to find effective and general factorizations. This paper presents a simple closed-form complete factorization of C-CSHTs based on that of R-CSHTs. The proposed factorization can be applied to both C- and R-CSHTs with one factorization and it provides several benefits: 1) It can save total implementation costs for both C-CSHTs and R-CSHTs; 2) the generalized R-CSHT factorization significantly reduces its computational cost; 3) memory-saved local orientation detection of images can be achieved; 4) a fast direction-aware transform can be attained; 5) it clarifies that C- and R-CSHTs are closely related to common block transforms, such as the discrete Fourier transform (DFT), binDCT, and HT; and 6) it achieves a new integer complex-valued transform, which can approximate the DFT better than the original C-CSHT. The image orientation estimation and performance in image coding of our R-CSHTs were evaluated through examples of practical applications based on the proposed factorization.

Multiplierless lifting based FFT via fast Hartley transform

The multiplierless fast Fourier transform (FFT) with dyadic-valued (rational) coefficients is important for many signal processing tools. The proposed lifting based FFT (L-FFT) based on fast Hartley transform (FHT) has a simpler structure than existing ones because fewer lifting steps need to be approximated. In addition, it has a structure of real-valued calculation followed by complex-valued parts, thereby it requires fewer memories for the internal implementation than the conventional FFTs.

Adaptive directional lifting wavelet-based lossless image coding with directional data hiding

This paper introduces a secure image coding method using adaptive directional lifting wavelet transform (ADLWT)-based lossless image coding with directional data hiding. ADLWT is an image dependent directional wavelet transform that provides high image compression performance. Since the lifting directions of ADLWT can be utilized as encryption key for decoding a correct image, the image can be protected from the illegal use by hiding the direction data into wavelet domain. We embed the directional data with the subband replacement method and the spread spectrum method into suitable regions so that the resulting bit rate is not increased. Experimental results show the proposed method can hide direction data with comparable bit rate of the conventional ADLWT-based image coding.

A two-dimensional non-separable implementation of dyadic-valued cosine-sine modulated filter banks for low computational complexity

This paper aims to design a new two-dimensional (2D) non-separable implementation of dyadic-valued cosine-sine modulated filter banks (2D D-CSMFBs) for low computational complexity. CSMFBs satisfy rich directional selectivity (DS) and shift-invariance (SI), and they can be easily designed by the modulation of a prototype filter. In addition, our previous work introduced a one-dimensional (1D) D-CSMFBs (1D D-CSMFBs). By restricting real-valued filter coefficients to rational-valued ones, they can save computational cost while keeping DS and SI. The proposed 2D implementation in this paper can further reduce the computational cost by unifying the conventional 2D separable structure into a 2D non-separable one directly. Furthermore, experimental results of image non-linear approximation show that the proposed 2D D-CSMFBs are comparable or even better than the 1D D-CSMFBs.

Multiplierless lifting-based fast X transforms derived from fast Hartley transform factorization

This paper presents M-channel (

Image boundary extension with mean values for cosine-sine modulated filter banks

M=2^{N}

A regularization approach for bayer reconstruction in lossy image coding by inverse demosaicing

M=2N,