Enhanced detectability of small objects in correlated clutter using an improved 2-D adaptive lattice algorithm

Abstract

Two-dimensional (2-D) adaptive filtering is a technique that can be applied to many image processing applications. This paper will focus on the development of an improved 2-D adaptive lattice algorithm (2-D AL) and its application to the removal of correlated clutter to enhance the detectability of small objects in images. The two improvements proposed here are increased flexibility in the calculation of the reflection coefficients and a 2-D method to update the correlations used in the 2-D AL algorithm. The 2-D AL algorithm is shown to predict correlated clutter in image data and the resulting filter is compared with an ideal Wiener-Hopf filter. The results of the clutter removal will be compared to previously published ones for a 2-D least mean square (LMS) algorithm. 2-D AL is better able to predict spatially varying clutter than the 2-D LMS algorithm, since it converges faster to new image properties. Examples of these improvements are shown for a spatially varying 2-D sinusoid in white noise and simulated clouds. The 2-D LMS and 2-D AL algorithms are also shown to enhance a mammogram image for the detection of small microcalcifications and stellate lesions.

2-D Iteratively Reweighted Least Squares Lattice Algorithm and Its Application to Defect Detection in Textured Images

“…No restrictions are imposed on their design since no spectral assumptions are required [3,4,7]. The input-output relation of the n-th stage can be explicitly written as follows: …”

“…2-D lattice filter is a digital filter that has been developed extending the structure of 1-D lattice filter to 2-D. With the attractive features stated [1][2][3][4][5][6][7][8], the 2-D lattice filter has been the center of interest in this study as an effective tool for modeling the input data as an AR process.…”

“…Motivated by the success of the RLSL algorithm in [7], we developed an iteratively reweighted least squares lattice (IRLSL) algorithm which is robust to outliers using the concepts of robust estimation methods [11]. Even though robust estimation methods are not new in literature, to the best of our knowledge they have not been used in the context of 2-D lattice filters which have many attractive features and are common structures in signal and image processing applications.…”

“…Ffrench et.al. [7] have developed a recursive least squares lattice (RLSL) type adaptive algorithm for the twelve-parameter 2-D lattice filter and applied it on the detection of small objects in correlated clutter. They have shown that RLSL algorithm provides the exact least squares solution for a single stage lattice filter.…”

“…Each stage is a multi-input/multi-output structure defined in terms of reflection coefficients. The reflection coefficients can be calculated either directly solving normal equations [1][2][3] or recursively by adaptive methods [4][5][6][7][8]. The algorithms developed for the adaptation of the lattice parameters are either gradient-based [4][5][6] or ________________________________________________________________________________ *This work has been partially supported by Turkish Technology Development Foundation under contract number recursive least squares (RLS) type [7][8] algorithms.…”