# Estimating Sparse Signals Using Integrated Wideband Dictionaries

## TL;DR

This paper presents a wideband dictionary framework for sparse signal estimation that improves accuracy and reduces computational cost by iteratively refining the parameter space, applicable to one- and multi-dimensional signals.

## Contribution

The proposed integrated wideband dictionary approach enables efficient sparse signal estimation with fewer dictionary elements and iterative refinement, outperforming traditional methods.

## Key findings

- Enhanced estimation accuracy demonstrated in numerical examples.
- Reduced computational complexity compared to traditional large dictionaries.
- Applicable to both one- and multi-dimensional signals.

## Abstract

In this paper, we introduce a wideband dictionary framework for estimating sparse signals. By formulating integrated dictionary elements spanning bands of the considered parameter space, one may efficiently find and discard large parts of the parameter space not active in the signal. After each iteration, the zero-valued parts of the dictionary may be discarded to allow a refined dictionary to be formed around the active elements, resulting in a zoomed dictionary to be used in the following iterations. Implementing this scheme allows for more accurate estimates, at a much lower computational cost, as compared to directly forming a larger dictionary spanning the whole parameter space or performing a zooming procedure using standard dictionary elements. Different from traditional dictionaries, the wideband dictionary allows for the use of dictionaries with fewer elements than the number of available samples without loss of resolution. The technique may be used on both one- and multi-dimensional signals, and may be exploited to refine several traditional sparse estimators, here illustrated with the LASSO and the SPICE estimators. Numerical examples illustrate the improved performance.