The ASAR GSV estimates were smaller as a result of correspondence with coastlines (not visible in Figure 7). The ASAR GSV expresses the GSV within the 1 km 2 pixel regardless of the land cover; hence, the fraction of water in coastline pixels resulted in a smaller retrieved GSV compared to the water fraction it had been accounted for. Larger GSV estimates were encountered primarily in two regions located along the south-east coast and the center-east part of the country (see ASAR and kNN maps of GSV in Figure 7 at latitudes of 57°N and 63°N, respectively). To verify whether the larger GSV estimates were a consequence of an imperfect constraint to the range of GSV to be retrieved with the BIOMASAR algorithm, the retrieval was repeated for different values of the maximum retrievable GSV. The effect on the retrieval was negligible, indicating that the difference was not related to the algorithm but rather likely to be structural. This interpretation was further supported by the strong similarity between the kNN and the NFI GSV estimates at 0.5°. It could have been argued that the larger GSV obtained with the ASAR data had its origin in the different scales of the datasets (0.03 ha for NFI, 0.06 ha for kNN and 100 ha for ASAR). The retrieved GSV is equivalent to the GSV of a 1 km 2 large cluster of trees where the individual forest components and other land cover features have been blended and considered as a forest unit as a whole. A 1 km GSV estimate derived from the NFI measurements or the kNN estimates was set to an average of individual GSV values within the 1 km window, each being representative of a small cluster of trees. To match with the definition of GSV of a 1 km ASAR pixel, the average also included non-forested, i.e., 0 m 3 /ha, pixels. As a consequence, the effect of different scales would then become more apparent in case of spatial heterogeneities of the land-cover, e.g., in case of fragmented landscapes of forest and other land cover types within the 1 km pixel of the ASAR imagery. Considering only areas with a small forest cover fraction within an ASAR pixel resulted in larger discrepancies between ASAR and kNN GSV (Figure 5). When restricting the analysis to pixels with a forest cover fraction greater than 90% the agreement statistics were r = 0.70, relative RMSD = 34.6% and bias = 19 m 3 /ha. These statistics are only slightly better compared to the values reported in Table 4 for all pixels because of the very large proportion of areas with unbroken forest cover in Sweden.
In CentralSiberia, the size of an ASAR pixel was comparable to the size of the field inventory sample units of the ten forest enterprises. Thus, we expected less influence of scales on the inter- comparison between the ASAR and the forest field inventory GSV. For the original resolution of the ASAR data, the retrieved GSV showed large spread along the 1:1 line when compared to the field inventory GSV and a tendency to saturate at 300 m 3 /ha (Figure 3). The retrieval statistics for the ten forest enterprises in Irkutsk Oblast at 0.01° (r = 0.46, relative RMSD = 41%, bias = −8 m 3 /ha) were in line with the numbers obtained for four forest enterprises in Krasnoyarsk Kray where the retrieval algorithm had been validated (r = 0.65, relative RMSE = 34%, bias = −8 m 3 /ha) . In contrast to the Swedish data, we could not assess the impact of the fraction of forest cover in a pixel since the field inventory data were at the same scale as the SAR data. Hence, the spread between the datasets should be primarily related to the weak sensitivity of the C-band backscatter to forest GSV, which is caused by the limited penetration of the microwave into the forest canopy. A multi-temporal combination served to reduce the impact of environmental conditions and residual speckle noise inherent in each observation on the retrieval but could not decrease the uncertainty of the estimation, which is embedded in the remote sensing measurement itself.
2.2. ALOS PALSAR
Spatially explicit estimates of GSV with a pixel size of 25 m were obtained from Advanced Land Observing Satellite (ALOS) Phased Array type L-band SAR (PALSAR) images. ALOS PALSAR operated between 2006 and 2011 at L-band (wavelength of 23 cm) with a pre-defined acquisition plan aiming, among other, at a yearly wall-to-wall coverage of forests. The PALSAR dataset consisted of four yearly mosaics of the radar backscattered intensity acquired during summer and fall between 2007 and 2010 in the Fine Beam Dual (FBD) mode. In FBD mode, PALSAR acquired co-polarized (HH) and cross-polarized (HV) signals. For each year, the mosaic included images of the radarbackscatter acquired during summer and fall because unfrozen conditions cause the backscatter to be most sensitive to forest structural parameters . The PALSAR mosaics were obtained after SAR long strip processing, ortho-rectification, slope correction and neighboring strip suppression . The mosaics were provided through JAXA’s Kyoto and Carbon Science Initiative  in a ready-to-use format. 2.3. ENVISAT ASAR
SAR sensors have certain advantages over optical sensors. They are active sensors that transmit their own energy and record the echoes reflected off the Earth’s surface (Campbell & Wynne 2011). Their use is therefore not constrained by the time of day and missions using active microwave sensors can be scheduled during unsatisfactory times for optical sensors (Horritt 1999). Because they use longer wavelengths in the microwave region of the electromagnetic spectrum, images are not severely affected by atmospheric attenuation such as clouds and light rain (Horritt 1999). SAR images are also sensitive to small scale surface roughness, soil moisture and slope (Kussul, Shelestov & Skakun 2008). The properties of the transmitted energy are also known, since it is generated by the sensor itself. The transmitted energy can therefore be compared to the received energy to determine characteristics of the illuminated surface (Campbell & Wynne 2011). A SAR image represents the backscattered power received by the antenna from the targeted area on the Earth’s surface. This backscatter is the portion of the transmitted signal returned towards the antenna (Campbell & Wynne 2011). The backscatter values of each pixel in the SAR image are often converted to a physical quantity known as the backscattering coefficient or the normalised radar cross section and expressed in decibel (dB) (Lillesand, Kiefer & Chipman 2008). The strength of the returned backscatter depends on the characteristics of the target on the Earth’s surface as well as the properties of the SAR systems (Campbell & Wynne 2011).
Mapping of burn areas and severity has been previously performed using polarimetric syntheticapertureradar to varying degrees of success. An early attempt by Kasischke et al. (1992) looked at the double bounce component of the backscatter signal to determine burn area in black spruce forest, reasoning that there will be a high return from exposed ground and tree trunks due to defoliation relative to unburned areas. More recent studies have sought to utilize combinations of polarimetric SAR data to better reveal burn areas and severity. Some studies have used SAR data as a complement to optical data, by providing information where there might otherwise be gaps in the optical data due to obscuration and by enhancing the spectral image with more physical information (Bernhard et al. 2011; Bernhard et al. 2012). Another data fusion technique utilized UAVSAR data in conjunction with National Land Cover Database information, segmenting the entropy/anisotropy/alpha angle
ionospheric imaging using spaceborne SAR has great advantages, including: (1) 2 ‐D images with relatively high spatial resolutions (subkilometers to kilometers), (2) global coverage, and (3) cost effectiveness, with one mission for both land and ionospheric observations. One disadvantage of the presented polarimetric approach is the need of full polarization measurements in four components (defined by polarization orientations of signal transmission and recep- tion). This demands more sophisticated system than single or dual polarizations, and high‐rate data downlink as well as large onboard storage. Using Tracking and Data Relay Satellite System (TDRSS, http://esc.gsfc.nasa.gov/space‐ communications/tdrs.html) and infrastructural upgrade of the ground segment, one could improve the data downlink significantly to accommodate the observation requirements. It is also desired to explore techniques that reduce the requirements of full polarization. Nevertheless we expect that SAR ionospheric imaging will become a great resource for future observations of ionospheric inhomogeneities and will also provide the required ionospheric correction to SAR and InSAR data for Earth observations.
The correction of the Faraday rotation simply involves coun- terrotating the data once Ω has been measured, which has prompted the development of several algorithms to estimate Ω from polarimetric SAR data –. These estimates are also of interest in their own right since (1) indicates that they allow the TEC to be measured. The sensitivity of the BIOMASS signal to the Faraday rotation will thus enable ionospheric struc- ture and dynamics to be routinely monitored along the satellite’s dawn–dusk orbit, which cuts across such important ionospheric features as the midlatitude trough and the auroral oval . Furthermore, proposed methods for correcting scintillation ef- fects in SAR images require accurate estimates of the Faraday rotation , .
A solution to the cross range resolution problem was first devised by Carl Wiley in the 1950s, known as Doppler beam sharpening . Doppler beam sharpening is now known as strip-mapping SAR, where the radar antenna is mounted orthogonal to the aircraft flight path and pulses are transmitted and collected as it passes the target scene, as shown in Figure 2.2. Each of these returns are combined and processed to form a return from a much larger “syntheticaperture.” For this strip-mapping syn- thetic aperture, the largest possible physical antenna beamwidth is desired, in order to maximize the number of returns for a specific point in space as the radar moves. This is opposite to the standard radar convention. An antenna’s beamwidth is typi- cally inversely proportional to its physical aperture size. This means where standard radar desires a large physical antenna, as described in Section 2.1.2, a synthetic aper- ture radar works best with the smallest physical antenna size possible. However, the required sampling rate to prevent aliasing provides a lower bound for how small the antenna can be, as samples must be acquired at least every half-width of the physical antenna.
Med sateliti, ki krožijo okrog našega planeta, so tudi tisti, na katere so nameščeni radarji z umetno odprtino (angl. SyntheticApertureRadar – SAR). Radarji z umetno odprtino se uporabljajo za skeniranje površja Zemlje. Odporni so proti vremenskim pojavom, kot so dež, oblačnost, toča itd. Tehnologija teh radarjev je namenjena predvsem zanesljivemu spremljanju dinamičnih procesov na Zemlji. Radar deluje tako, da meri razdaljo med senzorjem in točko na površini Zemlje, kjer se signal odbija nazaj. Valovna dolžina senzorja določa globino penetracije prenesenega signala v rastlinski sloj terena. Zaradi vseh prednosti se ta vrsta radarja uporablja za radarsko fotografiranje površin in se namešča na izvidniška letala, satelite in vesoljske sonde . Do sedaj je bilo razvitih kar nekaj SAR radarjev, ki delujejo na različnih frekvencah oz. v pasovih L, C in X (Slika 1).
However, the image formed by SLAR is poor in azimuth resolution. For SLAR the smaller the azimuth beamwidth, the ﬁner the azimuth resolution. In order to obtain high-resolution image one has to resort either to an impractically long antenna or to employ wavelengths so short that the radar must contend with severe attenuation in the atmosphere. In airborne application particularly the antenna size and weight are restricted. Another way of achieving better resolution from radar is signal processing. SyntheticApertureRadar (SAR) is a technique which uses signal processing to improve the resolution beyond the limitation of physical antenna aperture . In SAR, forward motion of actual antenna is used to ‘synthesize’ a very long antenna. SAR allows the possibility of using longer wavelengths and still achieving good resolution with antenna structures of reasonable size.
SyntheticApertureRadar (SAR) is a type of radar which is used in different weather conditions (clouds, fog or precipitation etc) and at different times (image can be acquired during day as well as night) to acquire a high resolution aerial and space based imaging of a terrain. The main reason to choose the SAR image instead the optical imaging devices (e.g. a camera) is the SAR ability to acquire the image of the terrain surface in all weather conditions and all times at day or night. On the other hand the optical devices work only in the day time and cannot work in bad weather conditions. There are two main types of platform; the satellites and the aircrafts. Sensors carried on the satellites have the ability to reach each point on the Earth's surface and offers a repetitive and systematic image collection. It needs high power requirements which lead to a high cost. Satellite sensors are restricted to a certain part of the earth and certain time dedicated by their orbits. On the other hand the sensors carried on the air crafts has the facility to monitor any part of the earth at each time and have low power requirements but have a restriction on the swath on the covered area. Satellite orbits are selected based on the capability and objective of the sensor or sensors they carry. Orbit selection means choosing the orbit parameters like altitude and inclination and rotation direction relative to the Earth which serve the mission objectives.
Bistatic SAR is considered as a very effective tool for exploring different geometrical configurations. The spatial separation of the transmitter and receiver not only allows different data acquisition geometries but also provides more information content of the imaging scene. The location of transmitter and receiver on different platforms has sev- eral advantages over monostatic SAR systems. Analysis and classification of objects in bistatic SAR has improved based on their backscattering characteristics. Different ex- periments have been performed and processing algorithms have been implemented over the years -. The first series of hybrid bistatic experiments with spaceborne trans- mitter and airborne receiver were conducted by USA in the mid nineties using ERS-1 satellite and SIR-C space shuttle as transmitter with airborne receivers . Due to limi- tation in technology and bistatic processing algorithms, less interest was seen in the bistatic area. With the proposal of interferometric cartwheel  in 2001, several bistatic SAR experiments , - were conducted with great interest. FHR has performed airborne bistatic experiments in 2003, using their AER-II as airborne trans- mitter and PAMIR as airborne receiver . In 2007, DLR conducted hybrid bistatic experiment using their TerraSAR-X satellite as transmitter with F-SAR airborne receiv- er . During 2008 and 2009, FHR performed hybrid bistatic SAR experiments, using TerraSAR-X satellite as transmitter and PAMIR as airborne receiver -.
Until the 50s imaging radars were denoted as SideLooking Airborne Radar (SLAR) and did not use the principle of syntheticaperture which is based on the generation of an effective long antenna by signal processing means rather than by the actual use of a long physical antenna. The SLAR has moderate azimuth resolution which deteriorates as the range increases. In SAR, the resulting azimuth resolution becomes equal to half the azimuth antenna length and is independent of the range distance . SAR systems have many advantages over the optical systems due to their all weather capability and the possibility to operate through smoke and at night. Further, SAR systems have the ability to penetrate long depth into vegetation and soil, and image the interior of the targets. With the SAR platform moving during the data collection, the range to a target changes so that the phase of the return echo is changed from position to another in the crossrange direction, where the spatial Doppler frequency is determined as the derivative of this phase history. Tracking this phase history over the length of syntheticaperture allows focusing the received echoes in crossrange . The SAR platform transmits a plane wave which reaches a point target; the latter becomes a secondary source emitting upward wave back toward the SAR platform.
The rotation transformation is usually implemented for all the pixels. However, for some targets, the transformation is not rational enough. Take the window shown in Fig. 3 as an example. This window includes two pixels with the same π/10 dipole model and two small areas with the uniform distribution volume scattering model. In this window, the actual double bounce scattering is 0%. The double bounce scattering power contribution calculated by the Y4, Y4R, and G4U methods for this window are shown in Fig. 3. Here, the performance of the decomposition without rotation transformation is better in this case. This example indicates that the rotation transformation is not always rational. For a certain pixel, if we have a judgment on the rationality and necessity before implementing a rotation transformation, the decomposition performance can be possibly improved.
 A Rajamani and V Krishnaveni in 2014 analyzed a survey of Various SAR Image Despeckling Techniques” consider various techniques of speckle reduction and their merits and demerits. A detailed comparative study of standard spatial domain speckle filters and wavelet domain speckle filters with respect to several metrics have been discussed. The recent developments usingadvanced image processing concepts such as patch similarity, statistical modeling, Graph cut methods total variation minimization method and compressed sensing methods have been presented. It has been planned to solve the limitations of increased computational complexity in a better way.  Deepika Hazarika etal. in 2015 purposed “A Lapped Transform Domain Enhanced Lee Filter with Edge Detection for Speckle Noise Reduction in SAR Images” described methods which are used Lapped orthogonal transform (LOT) domain adaptive enhanced Lee filter for despeckling SAR images. For edge preservation during despeckling process, the modified ratio of averages (MROA) edge detector is applied to the approximation subband to obtain edge information which is then employed in the proposed framework to obtain edge information in other subband. The proposed despeckling filter shows significant improvement over enhanced Lee filtering in spatial and wavelet domain and also outperforms one recent undecimated wavelet domain method.
In Section II, the general SAR signal in the two-dimensional frequency domain is derived. In Section III, the approxima- tions made to this signal are analyzed. For approximations of an arbitrary number of terms, an expression is derived for the phase error at any point in the frequency support band. Simulated data is used to analyze the effects that these phase errors have on image focusing with different order approximations and varying SAR parameters. Section IV provides a guideline for determining the number of terms in the approximation required for properly focusing the SAR image. Finally, a generalized chirp-scaling SAR processing algorithm is derived that includes the appropriate number of terms.
On both TS-X and TD-X images, we can observe effect of rainfall on X-band SAR data, for instance, one can find some bright slicks in the large dark pattern area in both images. The rain band of Sandy is also clearly visible in the TD-X image (Fig. 6.14 (a)). In a previous study, Melsheimer et al.  investigate effects of rain cell on SAR imagery using SIRC/X-SAR data in multifrequency (L-, C-, and X-band) and multipolarization (HH, VV and HV). They summarized that the radarbackscatter over ocean in the presence of rain cells is mainly associated with three processes: (1) scattering and attenuation of radar microwaves by hydrometeors in atmosphere, (2) the modification (enhancement or reduction) of sea surface roughness by rain drops, and 3) the enhanced sea surface roughness by wind gust. Generally, the latter two processes are easily identified in SAR imagery as both can significantly change the sea surface roughness. However, if the radar microwaves are attenuated by rain cell in atmosphere, it maybe not as clearly manifested in SAR image as other processes, particularly when rain fall has a large spatial coverage such as in hurricanes or typhoons. To quantify attenuation of radarbackscatter induced by rain fall, Urlaby  proposed a radiative transfer model for C-band radar. Danklmayer and Chandra  present a model to quantify the attenuation for Ka- and X- band SAR. This two-way path attenuation model is given as:
SyntheticApertureRadar (SAR) is a well-proven powerful remote sensing technique that can obtain high-resolution im- ages by using transmitted wide band waveforms and exploiting the relative motion between platform and targets. However, the conventional SAR systems make use of extremely low duty cycle coherent pulses to obtain both range and azimuth resolutions. Such pulsed radar systems usually have to transmit waveforms at a high power level and thus are of high cost and less compact. Therefore, they are hardly applicable to low- cost civil instruments such as unmanned aerial vehicle (UAV) or small aircraft solution . On the other hand, the single- antenna SAR systems cannot achieve high azimuth resolution and wide swath simultaneously. The tradeoff among many of the SAR system parameters results in a minimum antenna area constraint .
In linear algebra, the singular value decomposition (SVD) is an important factorization of a rectangular real or complex matrix, with several applications in signal processing and statistics. Applications which employ the SVD include computing the pseudo inverse, least squares fitting of data, matrix approximation, and determining the rank, range and null space of a matrix. SVD is a simple and valuable tool for analyzing image quality and the amount of independent information about the unknowns which can be reliably retrieved from observations in presence of noise. For spectrum estimation, it is generally possible to effectively overcome the associated problem due to nonuniform track distribution that may include significant noise propagation due to the ill-conditioned nature of the problem by Truncated Singular Value Decomposition (TSVD). In the following section, the mathematical description of the SVD and how to apply it to the spectrum estimation problem is presented.
are randomly distributed over the whole real numbers. ENVI software and its SARSCAPE module are used for pre-processing PALSAR datausing steps outlined by Mishra et al. . Focused PALSAR data is directly imported to extract single look complex (SLC) files which are multi- looked by a factor of 7 to improve radiometric resolution due to different resolutions in range and azimuth directions. Digital elevation model (DEM) is extracted using GO TOPO30 for the purpose of geo-referencing by nearest neighbor approximation. Phase-mod form of the geo-referenced data is then converted to complex files which are separated into real and imaginary parts. Band Math is then applied to extract normalized backscattering coefficient using the formula given in . The process is repeated for each polarization.