Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

Inversion of the Weyl integral transform and the radon transform on Rn using generalized wavelets

Abstract: We invert the Weyl integral transform by means of a generalized continuous wavelet transform on the half line associated with the Bessel operatorL α, α>−1/2. Next, we use the connection between radial classical wavelets onR n and generalized wavelets associated with the Bessel operatorL( n−2)/2 to derive new inversion formulas for the Radon transform onR n ,n≥2.

Image scrambling based on a new linear transform

Abstract: A new linear transform for scrambling images is proposed in this paper. The forward transform scrambles the image and the inverse transform unscrambles the image. We define transformation matrices for both scalar and blocked cases. Recursive and non-recursive algorithms based on the new transform are also proposed. The degree of scrambling or unscrambling can be determined by the user. The experimental results show that the positions of the pixels are strongly irregularized using the proposed transform. Unscrambling using a wrong key fails and results in an unintelligible image which cannot be recognized. We also show that the new transform provides a high level of image scrambling and is robust under common attacks and noise. The proposed linear transform is very simple and its implementation as triple-matrix multiplication is straightforward.

A novel CORDIC-based array architecture for the multidimensional discrete Hartley transform

Abstract: In this paper, a coordinate rotation digital computer (CORDIC)-based array architecture is presented for computing the multidimensional (M-D) discrete Hartley transform (DHT). Since the kernel of the M-D DHT is inseparable, the M-D DHT problems cannot be computed through the 1-D DHT's directly. Bracewell et al. have presented an algorithm for the M-D DHT through the 1-D DHT's. The existing hardware architectures have been designed using this algorithm. However, the postprocessing required in the algorithm leads to high hardware overhead. This paper presents a new algorithm to compute M-D DHT through a special 1-D transform which is derived through considering both the separable computation and the efficient implementation with CORDIC architectures. This algorithm provides a direct way to compute the M-D DHT separably through 1-D transforms with simpler postprocessing than that in Bracewell's approach. Also, the algorithm exploits the symmetry of the triangular functions to reduce the computational complexity. Using this algorithm, we design an array architecture for the M-D DHT. This architecture features a systolic computing style, PE's with a CORDIC structure, low I/O cost, and the encapsulated new M-D DHT algorithm. >