The Synthetic Aperture Radar (SAR) algorithm processes multiple radar returns from the target space to generate a single high-resolution image. Targets moving through the target space during the capture sequence will appear distorted on the final image. In addition, there is no velocity information that is calculated as part of the processing. The objective of this thesis is to develop techniques to determine the azimuth and range velocities of moving objects in the target space in the early stages of SAR processing. The typical SAR processing steps are Range Compressed, Range Doppler, and final image generation. The range velocity of a target can be determined after the Range Compression stage, and the azimuth velocity can be determined after the Range Doppler image is created. Calculating the velocity of a target without performing all the steps of the SAR process allows such information can be obtained quicker than the final image. This work is done as part of Cal Poly’s SAR Automatic Target Recognition (ATR) project, sponsored by Raytheon Space and Airborne Systems Division and headed by Professor John Saghri. The simulations performed as part of this thesis are done in a MATLAB simulation environment implementing a two-dimension SAR target space, first introduced in Brian Zaharris’ thesis. This work has expanded on this environment by introducing point target azimuth and range velocity detection.

The BIOMASS mission from the European Space Agency (ESA) is designed to measurebiomass and carbon content in Earth’s forests. To account for phase changes caused byionospheric variations, a map-drift autofocus algorithm is developed, which utilises a phasescreen of the ionosphere to eliminate phase errors in the signal. In this development, a filteris employed to integrate and remove noise from the second-order derivative of the ionosphericphase screen. This thesis aims to analyse methods to implement this filter andcompare their efficiency. Two filters are constructed using two methods, a Least Mean Square (LMS) filter and aWiener filter. Further emphasis is placed on the Wiener filter, and the most optimal way tocalculate it is explored in detail. The aim is to produce a filter that can integrate, lower theimpact of noise as much as possible and be computationally efficient. An implementationwas made in Python using simulated data of an ionosphere. The conclusion is that the Wiener filter can yield improved results if a precise estimation ofthe autocorrelation function of the ionospheric phase screen can be determined, and thatlinear regression models might be a method to do so. There is also consideration taken tothe noise of the data, it is compensated for by utilising multiple data sources. Additionally,to enhance computational efficiency, a comparison of different solving methods for the linearsystem of equations that is the filter where made, showing a LU-decomposition method tobe efficient.

A method of lensless, single pixel imaging is presented. This method, referred to as MAS-IPSII, is theoretically capable of resolutions as small as one quarter of the wavelength of the imaging light. The resolution is not limited by the aperture of any optic, making high resolutions (including subwavelength) feasible even at very large (greater than a meter) distances. Imaging requires only flat optics and a coherent source, making it a good candidate for imaging with extreme wavelengths in the UV and x-ray regimes. The method is demonstrated by the imaging of various test targets. Both real and complex imaging (i.e. holography) is demonstrated.

Antarctica is home to numerous perennially ice-covered (PIC) lakes that host rich benthic microbial ecosystems. These lakes are covered by a thick floating ice cover year-round and often have water columns supersaturated in dissolved gases, resulting in heavily bubbled ice covers, altering the optical properties of the ice and the amount of light that penetrates into the water column. Thus, understanding the optical properties of perennial lake ice can have important scientific implications to the study of life on Earth and the search for extraterrestrial life. Synthetic aperture radar (SAR) remote sensing has been used rigorously for over 50 years to study and monitor the seasonal response and long-term trends of backscatter over seasonally ice-covered (SIC) Arctic lakes. Limited studies have assessed the impacts of dissolved gases and ice/water interface bubbles on SAR backscatter variability over SIC lakes. The seasonal backscatter response of Antarctic PIC lakes remains unexplored; their physical nature asserts that their backscatter response should largely be decoupled from seasonal factors according to SIC lake backscatter theory. Additionally, gas supersaturated PIC lakes are ideal candidates to better understand the role of gas buildup and bubble formation on the backscatter response from floating ice covers. This thesis leverages a dense stack of Sentinel-1 C-band SAR imagery over Lake Untersee, a well-sealed PIC lake in East Antarctica, to explore the relationships between SAR backscatter and ice/water interface bubbles. This analysis integrates field measurements and temporal observations at the ice/water interface. Lastly, a brief comparative analysis extends to other ice covers, including moat-forming PIC lakes, as well as first-year and multi-year Arctic sea and lake ice. It is shown that Lake Untersee has a seasonal backscatter regime that is linked to air temperature. A strong correlation is found between the timing of backscatter intensity increase in winter and ice thickness. This relationship is attributed to variations in ice thickness which affect the length of the freezing period under the ice, the rate of dissolved gas accumulation, and ultimately, the nucleation and abundance of bubbles at the ice/water interface. These findings can be applied to other PIC lakes that have seasonal gas regimes. This research provides valuable insights into the complex interplay between ice cover characteristics, gas dynamics, interface bubbles, and SAR backscatter, enhancing our understanding of polar aquatic ecosystems and their broader implications for global environments.

For some time now, there has been a growing awareness in society about climate change, pollution, energy and the use of natural resources. This thinking has permeated society, mainly because the extreme natural phenomena that we are experiencing nowadays are no longer outliers in our time series of meteorological records. In this regard, it has been proven that the actual high temperatures are not only unparalleled, but also consistent around the globe which is something that had not happened until now (Neukom et al., 2019). The XX century was a turning point when it comes to the increase of the landuse for crops. In a context where the population doubled, the crop production for food from 1960 to 2010 tripled, helping to reduce the hungry population. When the world’s population is expected to continue to grow up to 9 billion people (Goodfray et al., 2010) by middle XXI century, it is essential to provide ourselves with the necessary tools to maximise crop production by taking advantage of all the resources available under a sustainable point of view. Under this context, all farmers in the European Union (EU) have the possibility to benefit from the Common Agricultural Policy (CAP), which came into force in 1960. The CAP is responsible for the financing of aid to farmers on a cross-compliance basis, based on the declaration of crop types. Traditionally, the authorities have checked the veracity of declarations in person through field inspections, which is clearly a highly inefficient, impractical and very expensive system. However, in 2018 the European Commission drafted an amendment to the CAP (European Commission, 2018), to be implemented in 2020, recommending the establishment of newprocedures for checking declarations, including the use of satellite data from the Copernicus programme or other new technologies. Among the various satellite technologies, Synthetic Aperture Radar (SAR) (Brown,1967; Curlander and McDonough, 1992) has proven the most reliable,as the images are acquired with a constant pass period and they are not subject to cloud problems (as is the case with sensors working in the optical domain) and information can be acquired both day and night. They are based in a SAR microwave sensor installed on a satellite platform with a forward trajectory which offers side-looking imaging geometries. Working in a range between 300 MHz and 30 GHz, the SAR sensor is in charge of emitting electromagnetic pulses and receiving the resulting echoes from the imaged target, which can help retrieve information about its dielectric properties, geometry, orientation, shape, and its behaviour along time. For a given target, the SAR backscattering response σ0 is function of many parameters (Lee and Pottier, 2017; Dobson et al., 1985): wave frequency, polarisation, imaging configuration, roughness, geometrical structure and dielectric properties. This makes the information extraction a major problem, as identical radar responses from two different targets may lead to the same result. To cope with this problem, the main techniques are based on extending the observation space by working with the full diversity of data. Thus, the main axes of SAR data are: • Time • Polarimetry • Interferometry • Frequency. Time series of radar data constitutes a major source of information for the classification of crops and land cover, since it makes it possible to distinguish between classes by their temporal behaviour: some land covers show a uniform response along time (e.g. urban areas), whereas there are others subject to seasonal changes (e.g. crops). It may happen that different crop species give the same radar response at a given time, however, when the time window becomes larger, and consecutive acquisitions are taken over a shorter time span, the more one can detect abrupt changes in the target over a longer time interval. Polarimetry is sensitive to the shape, orientation and the scattering mechanisms of the scatterers (Boerner et al.,1981; Zyl, Zebker, and Elachi, 1987). In that sense, when using different polarisations it is possible to discern better the true nature of the target, as some features may be visible in one polarisation but not in the others. Regarding multi-spectral data, it also constitutes a major source of information which can be exploited for classification purposes. Working with sensors operating at different frequencies, or wavelengths, provides diversity in the size of the elements of the scene to which the radar is sensitive as the radar backscattering will come from elements the size of the wavelength used it. For all of the above, multifrequency data provide complementary information, as each frequency operates and interacts with elements of the same wavelength or longer, and being transparent to all others. In addition, different bands are also associated with different spatial resolutions, so a high-frequency sensor can complement the classification performance of a low-frequency sensor when there are sufficiently small details in the scene that cannot be appreciated with the spatial resolution available at the lower frequency. From all the 4 axes exposed above, Interferometry (Graham, 1974) is without a doubt the least exploited for classification purposes. While polarimetry is sensitive to the scattering mechanisms of the scene by means of the polarisation information, interferometry adds the third dimension by being sensitive to the spatial distribution of the scatterers (Treuhaft et al., 1996). Coherence and phase difference computed between two complex-valued SAR images are the main descriptors of interferometry (Bamler and Hartl, 1998), and together, can be used to derive topographic information, vegetation structure, and deformation (volcanoes, landslides, etc.). For this reason, interferometry is especially suited for classification of covers in which there is vertical distribution of elements, e.g. urban areas and vegetation (forests and crops). Polarimetric interferometric SAR (PolInSAR) (Cloude and Papathanassiou, 1998; Treuhaft and Cloude, 1999), constitutes the next step forward, and is based on the application of interferometry to all polarisation channels. Polarimetry can identify the different scattering mechanisms in the scene by using the polarisation information, whilst interferometry is able to locate the effective scattering phase centres, which are mainly dependent on frequency, the polarisation employed, the physical, geometrical structure and orientation of the scatterer. By using the combination of both we can retrieve the vertical structure of the scene, which shows a great potential for classification purposes, since classes characterised by similar backscattering or polarimetric responses can be separated if their heights are different (e.g. types of buildings, forests, crops, etc.), whereas classes with similar heights, and hence similar interferometric coherence values (e.g. grass, crops, bare soil, etc.) can be resolved using their polarimetric response. In summary, PolInSAR-based classification is attractive since polarimetric ambiguities are resolved by interferometric information and vice-versa. The lack of exploitation of the 4 data axes in the literature, plus the arrival of a new generation of SAR sensors in the near future such as ROSE-L, BIOMASS and NISAR among others, offers a new range of possibilities in terms of new types of features for classification whose results and impact must be analysed. In this context, there are many types of SAR data (i.e. features) that have not been used yet, acquired from different sensors (Sentinel-1, PAZ, TanDEMX, TerraSAR-X and ALOS-2), and whose diversity axes, either used individually or jointly, have not yet been explored for classification applications. Therefore, the exploration of these new types of SAR data, whose contribution to classification is unknown regarding crop-type mapping, is the main objective of this doctoral thesis, and consequently also its main novelty. Based on the current state of the art of the research topic the main objective of this PhD thesis is to explore the added value of new SAR features, and their potential, alone or used together, for crop type and land cover classification. In the end, several experiments will be carried out, in different test sites, in which the proposed new features will be evaluated and compared with the traditional observables used so far, with the aim of evaluating their internal potential in classification applications. / Work supported by the Spanish Ministry of Science and Innovation, the State Agency of Research (AEI) and the European Funds for Regional Development (EFRD) under Projects TEC2017-85244-C2-1-P and PID2020-117303GB-C22. Mario Busquier received a grant from the University of Alicante UAFPU20-08.

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