An algorithm for discrete fractional Hadamard transform

We present a novel algorithm for calculating the discrete fractional Hadamard transform for data vectors whose size N is a power of two. A direct method for calculation of the discrete fractional Hadamard transform requires $N^2$ multiplications, while in proposed algorithm the number of real multiplications is reduced to $N$log$_2N$.Comment: 22 pages, 4 figure

A Generalised Hadamard Transform

A Generalised Hadamard Transform for multi-phase or multilevel signals is introduced, which includes the Fourier, Generalised, Discrete Fourier, Walsh-Hadamard and Reverse Jacket Transforms. The jacket construction is formalised and shown to admit a tensor product decomposition. Primary matrices under this decomposition are identified. New examples of primary jacket matrices of orders 8 and 12 are presented.Comment: To appear in the proceedings of the 2005 IEEE International Symposium on Information Theory, Adelaide, Australia, September 4-9, 200

Development and evaluation of a Hadamard transform imaging spectrometer and a Hadamard transform thermal imager

A spectrometric imager and a thermal imager, which achieve multiplexing by the use of binary optical encoding masks, were developed. The masks are based on orthogonal, pseudorandom digital codes derived from Hadamard matrices. Spatial and/or spectral data is obtained in the form of a Hadamard transform of the spatial and/or spectral scene; computer algorithms are then used to decode the data and reconstruct images of the original scene. The hardware, algorithms and processing/display facility are described. A number of spatial and spatial/spectral images are presented. The achievement of a signal-to-noise improvement due to the signal multiplexing was also demonstrated. An analysis of the results indicates both the situations for which the multiplex advantage may be gained, and the limitations of the technique. A number of potential applications of the spectrometric imager are discussed

Using the discrete hadamard transform to detect moving objects in surveillance video

In this paper we present an approach to object detection in surveillance video based on detecting moving edges using the Hadamard transform. The proposed method is characterized by robustness to illumination changes and ghosting effects and provides high speed detection, making it particularly suitable for surveillance applications. In addition to presenting an approach to moving edge detection using the Hadamard transform, we introduce two measures to track edge history, Pixel Bit Mask Difference (PBMD) and History Update Value (H UV ) that help reduce the false detections commonly experienced by approaches based on moving edges. Experimental results show that the proposed algorithm overcomes the traditional drawbacks of frame differencing and outperforms existing edge-based approaches in terms of both detection results and computational complexity

Improved analysis of the subsampled randomized Hadamard transform

This paper presents an improved analysis of a structured dimension-reduction map called the subsampled randomized Hadamard transform. This argument demonstrates that the map preserves the Euclidean geometry of an entire subspace of vectors. The new proof is much simpler than previous approaches, and it offers---for the first time---optimal constants in the estimate on the number of dimensions required for the embedding.Comment: 8 pages. To appear, Advances in Adaptive Data Analysis, special issue "Sparse Representation of Data and Images." v2--v4 include minor correction

A practical multi-spectrum Hadamard Transform Spectrometer

A Hadamard Transform Spectrometer (HTS) which simultaneously obtains fifteen infrared spectra, each having 255 spectral elements was constructed. Spectra are obtained essentially in real time through use of a minicomputer with 8K words of memory and a CRT display. This permits operation of the instrument in the field