In this paper, we develop a new method for weighted least squares 2D linear-phase FIR filter design. It poses the problem of filter design as the problem of projecting the desired frequency response onto the subspace spanned by an appropriate orthonormal basis. We show how to compute the orthonormal basis efficiently in the cases of quadrantallysymmetric filter design and centro-symmetric filte...

The mathematical and numerical least squares solution of a general linear system of equations is discussed. Perturbation and differentiability theorems for pseudoinverses are given. Computational procedures for calculating least squares solutions using orthonormal transformations, multiplying matrices by a matrix of orthonormal basis vectors for the null-space of a given matrix, sequential proc...

where each θj is supported only on Ω ⊂ {1, 2, . . . , N}, with |Ω| = K. The matrix Ψ is orthonormal, with dimension N × N (we consider only signals sparse in an orthonormal basis). We denote by Φj the measurement matrix for signal j, where Φj is of dimension M ×N , where M < N . We let yj = Φjxj = ΦjΨθj be the observations of signal j. We assume that the measurement matrix Φj is random with i.i...

We propose a constructive method to find compactly supported orthonormal wavelets for any given compactly supported scaling function φ in the multivariate setting. For simplicity, we start with a standard dilation matrix 2I2×2 in the bivariate setting and show how to construct compactly supported functions ψ1, · · · , ψn with n > 3 such that {2ψj(2x − `, 2ky − m), k, `,m ∈ Z, j = 1, . . . , n} ...

We describe extensions to the \best-basis" method to select orthonormal bases suitable for signal classiica-tion and regression problems from a large collection of orthonormal bases. For classiication problems, we select the basis which maximizes relative entropy of time-frequency energy distributions among classes. For regression problems, we select the basis which tries to minimize the regres...

The fusion of imaging model and differential geometric is used to research the recognition problem of blurred-image in this paper. According to some assumptions, the established subspace results from the convolution of an image with some complete orthonormal basis functions with a predefined maximum size. Therefore, we demonstrate that the corresponding subspace created from a clear image and i...

The mathematical and numerical least squares solution of a general linear system of equations is discussed. Perturbation and differentiability theorems for pseudoinverses are given. Computational procedures for calculating least squares solutions using orthonormal transformations, multiplying matrices by a matrix of orthonormal basis vectors for the null-space of a given matrix, sequential proc...

In a previous paper, one of us pointed out that the anomalous dimension matrices for all physical processes that have been calculated to date are complex symmetric, if stated in an orthonormal basis. In this paper we prove this fact and show that it is only true in a subset of all possible orthonormal bases, but that this subset is the natural one to use for physical calculations.

This paper explores the segmentation of tutorial dialogue into cohesive topics. A latent semantic space was created using conversations from human to human tutoring transcripts, allowing cohesion between utterances to be measured using vector similarity. Previous cohesionbased segmentation methods that focus on expository monologue are reapplied to these dialogues to create benchmarks for perfo...

Abstract. In order to get an efficient representation of images which contain orientated edges we construct a directional wavelet basis for L(R). The wavelets basis consists of Haar wavelets with compact support on triangles. In comparison with the classical wavelet transform our functions offer two more directions (diagonal directions). Applying our simple wavelet system to image denoising and...