Reconstruction of Two-Dimensional Signals from the Fourier Transform Magnitude.
Abstract
This thesis is concerned with the problem of reconstructing a discrete two-dimensional signal of known support from the Fourier transform magnitude only. This problem arises in many fields where imaging is desired, such as astronomy and wavefront sensing. Since the autocorrelation function is easily calculated from the Fourier transform magnitude, we attack the equivalent problem of signal reconstruction from a known autocorrelation function. The main result of the thesis is a new algorithm for realizing this reconstruction. This algorithm is guaranteed to yield the correct solution given accurate measurements and is much more computationally attractive than previous reconstruction algorithms. The result is based on the detailed analysis of the zeros of a polynomial which is essentially the two-dimensional z-transform of the known autocorrelation signal. From this analysis, a large numbers of zeros of the z-transform of the unknown discrete signal are extracted. This set of zeros is then used to extract the signal values via the solution of a set of linear equations. Examples of the application of this algorithm to several families of images is presented, along with a discussion of the accuracy and computational requirements of the new algorithm. We conclude with a discussion of the application of the ideas of this thesis to the area of two-dimensional filter design and stability testing. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1986
- Accession Number
- ADA168792
Entities
People
- David Izraelevitz
Organizations
- Massachusetts Institute of Technology