Hadamard transform

About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.

A Hadamard matrix of order 428

Abstract: Four Turyn type sequences of lengths 36, 36, 36, 35 are found by a computer search. These sequences give new base sequences of lengths 71, 71, 36, 36 and are used to generate a number of new T-sequences. The first order of many new Hadamard matrices constructible using these new T-sequences is 428. © 2004 Wiley Periodicals, Inc.

Methods and apparatuses for video segmentation, classification, and retrieval using image class statistical models

Abstract: Techniques for classifying video frames using statistical models of transform coefficients are disclosed. After optionally being decimated in time and space, image frames are transformed using a discrete cosine transform or Hadamard transform. The methods disclosed model image composition and operate on grayscale images. The resulting transform matrices are reduced using truncation, principal component analysis, or linear discriminant analysis to produce feature vectors. Feature vectors of training images for image classes are used to compute image class statistical models. Once image class statistical models are derived, individual frames are classified by the maximum likelihood resulting from the image class statistical models. Thus, the probabilities that a feature vector derived from a frame would be produced from each of the image class statistical models are computed. The frame is classified into the image class corresponding to the image class statistical model which produced the highest probability for the feature vector derived from the frame. Optionally, frame sequence information is taken into account by applying a hidden Markov model to represent image class transitions from the previous frame to the current frame. After computing all class probabilities for all frames in the video or sequence of frames using the image class statistical models and the image class transition probabilities, the final class is selected as having the maximum likelihood. Previous frames are selected in reverse order based upon their likelihood given determined current states.

Variational inequalities on Hadamard manifolds

Abstract: The notion of variational inequalities is extended to Hadamard manifolds and related to geodesic convex optimization problems. Existence and uniqueness theorems for variational inequalities on Hadamard manifolds are proved. A convexity property of the solution set of a variational inequality on a Hadamard manifold is presented.

Quadratic regularization functionals for phase unwrapping

Abstract: The problem of unwrapping a noisy principal-value phase field or, equivalently, reconstructing an unwrapped phase field from noisy and possibly incomplete phase differences may be considered ill-posed in the sense of Hadamard. We apply the Thikonov regularization theory to find solutions that correspond to minimizers of positive-definite quadratic cost functionals. These methods may be considered generalizations of the classical least-squares solution to the unwrapping problem; the introduction of the regularization term permits the reduction of noise (even if this noise does not generate integration-path inconsistencies) and the interpolation of the solution over regions with missing data in a stable and controlled way, with a minimum increase of computational complexity. Algorithms for finding direct solutions with transform methods and implementations of iterative procedures are discussed as well. Experimental results on synthetic test images are presented to illustrate the performance of these methods.