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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 select an orthonormal basis suitable for sig-nal/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)

Fig. IO. The noisy image for Example 4. obtained from the noi\y projec-tion\ of the Shepp-Logan phantom Fig. I I. MMSE image obtained by constraining the wavelet coefficients of the noisy image: Example 4. threshold is used to set the finest-scale coefficients to zero. The resulting MMSE image is shown in Fig. I 1 The noise power has been reduced by 20.3%… (More)

- Naoki Saito
- 2007

We propose a new method to analyze and represent data recorded on a domain of general shape in R d by computing the eigenfunctions of Laplacian defined over there and expanding the data into these eigenfunctions. Instead of directly solving the eigenvalue problem on such a domain via the Helmholtz equation (which can be quite complicated and costly), we… (More)

The authors previously developed the so-called local discriminant basis (LDB) method for signal and image classiÿcation problems. The original LDB method relies on diierences 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)

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)

We introduce a new local sine transform that can completely localize image information both in the space domain and in the spatial frequency domain. This transform, which we shall call the polyharmonic local sine transform (PHLST), first segments an image into local pieces using the characteristic functions, then decomposes each piece into two components:… (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… (More)