Maximum subarray algorithms for use in astronomical imaging

Abstract

The maximum subarray problem is used to identify the subarray of a two dimensional array, where the sum of elements is maximized. In terms of image processing, the solution has been used to find the brightest region within an image. Two parallel algorithms of the maximum subarray problem solve this problem in O(n) and O(log n) time. A field programmable gate array implementation has verified theoretical maximum performance, however extensive customisation is required restricting general application. A more convenient platform for this work is a graphics processor unit, since it offers a flexible trade-off between hardware customization and performance. Implementation of the maximum subarray algorithm on a graphics processor unit is discussed in this article for rectangular solutions and convex extensions are explored.

The Extraction of Maximal-Sum Principal Submatrix and Its Applications

“…The characteristics of existing methods for calculation are the maximum volume [8], the largest logarithm of the determinant and the minimal trace of the inverse of the selected principal submatrix, but we focus on the sum of all elements of the submatrix. The sum of the entries of submatrix Discrete N Unfixed Accurate [2] The sum of the entries of submatrix Discrete N Unfixed Approximate [3][4][5] The sum of the entries of submatrix Consecutive N Unfixed Accurate [6] The determinant of submatrix + Discrete Y Fixed Approximate [7] The sum of the entries of submatrix ++ Discrete Y Fixed Approximate [8] The Compared to the MSS extraction, the commonality of all methods is to find the optimal solution based on the sum of all elements of the submatrix, but most methods do not specify the size of the submatrix, and we, in this paper, focus on the k-order principal submatrix.…”

“…The theory, application, and algorithm on maximal-sum submatrix (MSS) have received a lot of attention recently [1,2]. The MSS problem, also known as the maximum subarray problem [3,4], is to find the submatrix that maximizes the sum of matrix elements in it. The solutions to many application problems, such as solving the rectilinear picture compression [5] and finding a subset of genes that is relatively highly expressed among a subset of patients [1], can be converted to finding the maximal-sum submatrix from a matrix.…”