Synthetic aperture radar is an important tool in a wide range of civilian and military imaging
applications. This is primarily due to its ability to image in all weather conditions, during
both the day and the night, unlike optical imaging systems. A synthetic aperture radar system
contains a step which is not present in an optical imaging system, this is image formation.
This is required because the acquired data from the radar sensor does not directly correspond
to the image. Instead, to form an image, the system must solve an inverse problem. In
conventional scenarios, this inverse problem is relatively straight forward and a matched lter
based algorithm produces an image of suitable image quality. However, there are a number of
interesting scenarios where this is not the case.
Scenarios where standard image formation algorithms are unsuitable include systems with
data undersampling, errors in the system observation model and data that is corrupted by radio
frequency interference. Image formation in these scenarios will form the topics of this thesis
and a number of iterative algorithms are proposed to achieve image formation. The motivation
for these proposed algorithms is primarily from the eld of compressed sensing, which considers
the recovery of signals with a low-dimensional structure.
The rst contribution of this thesis is the development of fast algorithms for the system
observation model and its adjoint. These algorithms are required by large-scale gradient based
iterative algorithms for image formation. The proposed algorithms are based on existing fast
back-projection algorithms, however, a new decimation strategy is proposed which is more
suitable for some applications.
The second contribution is the development of a framework for iterative near- eld image
formation, which uses the proposed fast algorithms. It is shown that the framework can be used,
in some scenarios, to improve the visual quality of images formed from fully sampled data and
undersampled data, when compared to images formed using matched lter based algorithms.
The third contribution concerns errors in the system observation model. Algorithms that
correct these errors are commonly referred to as autofocus algorithms. It is shown that conventional
autofocus algorithms, which work as a post-processor on the formed image, are unsuitable
for undersampled data. Instead an autofocus algorithm is proposed which corrects errors within
the iterative image formation procedure. The proposed algorithm is provably stable and convergent with a faster convergence rate than previous approaches.
The nal contribution is an algorithm for ultra-wideband synthetic aperture radar image
formation. Due to the large spectrum over which the ultra-wideband signal is transmitted, there
is likely to be many other users operating within the same spectrum. These users can produce
signi cant radio frequency interference which will corrupt the received data. The proposed
algorithm uses knowledge of the RFI spectrum to minimise the e ect of the RFI on the formed
image
