# An efficient methodology to estimate the parameters of a two-dimensional chirp signal model

## TL;DR

This paper introduces a computationally efficient method for estimating parameters of 2-D chirp models in image processing, matching the accuracy of traditional methods with improved speed.

## Contribution

It proposes a new estimation procedure that is faster than least squares and retains its asymptotic properties, extending to multi-component models with sequential estimation.

## Key findings

- Estimators are computationally more efficient than least squares.
- Proposed estimators have the same asymptotic properties as least squares.
- Simulation studies confirm satisfactory performance.

## Abstract

In various capacities of statistical signal processing two-dimensional (2-D) chirp models have been considered significantly, particularly in image processing$-$ to model gray-scale and texture images, magnetic resonance imaging, optical imaging etc. In this paper we address the problem of estimation of the unknown parameters of a 2-D chirp model under the assumption that the errors are independently and identically distributed (i.i.d.). The key attribute of the proposed estimation procedure is that it is computationally more efficient than the least squares estimation method. Moreover, the proposed estimators are observed to have the same asymptotic properties as the least squares estimators, thus providing computational effectiveness without any compromise on the efficiency of the estimators. We extend the propounded estimation method to provide a sequential procedure to estimate the unknown parameters of a 2-D chirp model with multiple components and under the assumption of i.i.d. errors we study the large sample properties of these sequential estimators. Simulation studies and a synthetic data analysis show that the proposed estimators perform satisfactorily.