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Article history: Received 14 December 2007 Revised 9 September 2008 Accepted 11 September 2008 Available online 25 September 2008 Communicated by Naoki Saito We present a condition on the matrix of an underdetermined linear system which guarantees that the solution of the system with minimal q-quasinorm is also the sparsest one. This generalizes, and(More)
We describe an extension to the “best-basis” method to select an orthonormal basis suitable for signal/image classification problems from a large collection of orthonormal bases consisting of wavelet packets or local trigonometric bases. The original best-basis algorithm selects a basis minimizing entropy from such a “library of orthonormal bases” whereas(More)
We introduce a randomized procedure that, given an m×n matrix A and a positive integer k, approximates A with a matrix Z of rank k. The algorithm relies on applying a structured l×m random matrix R to each column of A, where l is an integer near to, but greater than, k. The structure of R allows us to apply it to an arbitrary m× 1 vector at a cost(More)
We describe an extension to the \best-basis" method to construct an orthonormal basis which maximizes a class separability for signal classiication problems. This algorithm reduces the dimen-sionality of these problems by using basis functions which are well localized in time-frequency plane as feature extractors. We tested our method using two synthetic(More)
We propose a shift-invariant multiresolution representation of signals or images using dilations and translations of the autocorrelation functions of compactly supported wavelets. Although these functions do not form an orthonormal basis, their properties make them useful for signal and image analysis. Unlike wavelet-based orthonormal representations, our(More)
The authors previously developed the so-called local discriminant basis (LDB) method for signal and image classi3cation problems. The original LDB method relies on di4erences in the time–frequency energy distribution of each class: it selects the subspaces where these energy distributions are well separated by some measure such as the Kullback–Leibler(More)
In this paper we describe a new technique for detecting and characterizing ellipsoidal shapes automatically from any type of image. This technique is a single pass algorithm which can extract any group of ellipse parameters or characteristics which can be computed from those parameters without having to detect all five parameters for each ellipsoidal shape.(More)
Recently developed classification and regression methods are applied to extract geological information from acoustic well-logging waveforms. First, acoustic waveforms are classified into the ones propagated through sandstones and the ones propagated through shale using the local discriminant basis (LDB) method. Next, the volume fractions of minerals are(More)