Showing papers by "Joel A. Tropp published in 2003"

Improved sparse approximation over quasiincoherent dictionaries

Abstract: This paper discusses a new greedy algorithm for solving the sparse approximation problem over quasiincoherent dictionaries. These dictionaries consist of waveforms that are uncorrelated "on average," and they provide a natural generalization of incoherent dictionaries. The algorithm provides strong guarantees on the quality of the approximations it produces, unlike most other methods for sparse approximation. Moreover, very efficient implementations are possible via approximate nearest-neighbor data structures.

CDMA signature sequences with low peak-to-average-power ratio via alternating projection

Abstract: Several algorithms have been proposed to construct optimal signature sequences that maximize the sum capacity of the uplink in a direct-spread synchronous code division multiple access (CDMA) system. These algorithms produce signatures with real-valued or complex-valued entries that generally have a large peak-to-average power ratio (PAR). This paper presents an alternating projection algorithm that can design optimal signature sequences that satisfy PAR side constraints. This algorithm converges to a fixed point, and these fixed points are partially characterized.

Optimal CDMA signature sequences, inverse eigenvalue problems and alternating minimization

Abstract: This paper desribes the matrix-theoretic ideas known as Welch-bound-equality sequences or unit-norm tight frames that are used to alternate minimizing the total squared correlation. This paper shows the construction of an optimal signature sequences for the synchronous code-division multiple-access (S-CDMA) channel in the presence of white noise and uniform received powers to solve inverse eigenvalue problems that maximize the sum capacity of the S-CDMA channel.

The Metric Nearness Problem with Applications

Abstract: Many practical applications in machine learning require pairwise distances among a set of objects. It is often desirable that these distance measurements satisfy the properties of a metric, especially the triangle inequality. Applications that could benefit from the metric property include data clustering and metric-based indexing of databases. In this paper, we present the metric nearness problem: Given a dissimilarity matrix, find the “nearest” matrix of distances that satisfy the triangle inequalities. A weight matrix in the formulation captures the confidence in individual dissimilarity measures, including the case of altogether missing distances. For an important class of nearness measures, the problem can be attacked with convex optimization techniques. A pleasing aspect of this formulation is that we can compute globally optimal solutions. Experiments on some sample dissimilarity matrices are presented, including some from biology.