The Number of Looks in an Image

The number of looks in an intensity image is a measure of the statistical fluctuations introduced by speckle resulting from the interference between radnomly-positioned scatterers. It is purely a property of the imaging process and depends on the number of independent speckle estimates that have been combined to form the final image. For example, ERS PRI data is described as 3 look. This means that the final image has been formed by adding the intensitites from three independent single-look complex (SLC) components.

To reduce speckle levels even further, many people sacrifice the resolution of a single image and produce a smaller one in which each pixel is formed by averaging a clump of four pixels in the original (say). If the image is uncorrelated, this process increases the number of looks by a factor of four. Unfortunately, there is usually little redundant information in a SAR image (unlike the situation in optical images) because objects such as trees, vehicles and buildings typically occupy only at most one or two pixels (for currently available or envisaged satellite SAR systems).

The interaction between the ENL, the pixel spacing and the resolution must be understood. Let us first define these quantities.

Effective (Equivalent) Number of Looks

The statistics of the speckle are usually described in terms of the Effective (or Equivalent) Number of Looks (ENL). This is intended to represent the speckle component of the observed intensity. Normally, of course, the intensity combines both speckle and RCS fluctuations. However, if the underlying RCS is uniform the ENL can be defined as

$$\hbox{ENL} = \frac{\hbox{mean}^2}{\hbox{variance}}$$

In general estimating the looks measure yields values which are smaller than the true ENL because additional RCS fluctuations are included. Only if the RCS is constant, or if the observed intensity is divided by the true underlying RCS, would the looks measure correspond to the ENL.

Resolution

The physical characteristics of the radar determine how far apart two objects on the ground must be in order for them to be distinguished in the image. This minimum distance is the spatial resolution of the image. The resolution in the range (across-track) direction is determined by the bandwidth of the transmitted pulse: larger bandwidth equals higher resolution. The resolution in the azimuth (along-track) direction is determined by the length of the radar antenna: a shorter antenna gives a higher resolution.

Pixel spacing

The pixel spacing in an image is determined by the sampling frequency of the processor. An image can be oversampled so that the pixel size is smaller than the resolution. When this happens, the values of neighbouring pixels are correlated. To obtain independent samples the image must be averaged down until the pixel spacing is at least as large as the resolution.

If we now consider averaging the intensity in neighbouring correlated pixels the ENL will not be reduced by the expected amount because the speckle is correlated. ERS PRI data is described as having an ENL of 3.0. The pixel size is about $12.5\hbox{m} \times 12.5\hbox{m}$ and the resolution about $25\hbox{m} \times 25\hbox{m}$. Thus averaging 2x2 pixels does not result in an ENL of 12 but a value nearer 6.