Noise Reduction

Owned by Marco Peters
Last updated: 2020-11-12
5 min read

The Noise Reduction Tool is used to correct and remove the coherent noises, known as drop-outs and vertical striping, usually found in hyperspectral images acquired by push-broom sensors such as CHRIS.

Introduction

Hyperspectral images acquired by remote sensing instruments are generally affected by two kinds of noise. The first one can be defined as standard random noise, which varies with time and determines the minimum image signal-to-noise ratio (SNR). In addition, hyperspectral images can present non-periodic partially deterministic disturbance patterns, which come from the image formation process and are characterized by a high degree of spatial and spectral coherence. The objective of the Noise Reduction Tool is to correct or reduce these noise signals before any further processing.

  • Drop-outs: One of the errors affecting CHRIS images is the fact that transmission of CHRIS channel 2 (odd and even pixels from each CCD row are read in parallel) randomly fails producing anomalous values at the odd pixels in some image rows called drop-outs. Drop-outs hamper the operational use of CHRIS images since latter processing stages are drastically affected by these anomalous pixels. These errors must be identified and corrected by making use of both spatial and spectral information of the anomalous pixel and its neighbours.

  • Vertical striping: Another well-known problem of CHRIS images is a spatial coherent noise usually found in images acquired by push-broom sensors. This multiplicative noise in image columns comes from irregularities of the entrance slit of the spectrometer and CCD elements in the across-track direction (horizontal lines). Although the entire system was fully characterized after assembly, changes in temperature (due to the seasonal variation of the in-orbit CHRIS instrument temperature) produce a dilation of the slit that results in a complex vertical pattern dependent on the sensor's temperature, and thus it must be modelled and corrected.

Noise Reduction Algorithm

The algorithm implemented by the Noise Reduction Tool is described in detail by Gómez-Chova et al. (2008). In brief, the following steps are carried out:

Drop-out Correction

In CHRIS images, drop-outs can be seen as missing pixels with anomalous values (usually zero or negative values). These invalid values are detected and replaced by a weighted average of the values of the neighboring pixels. In order to avoid the poor performance of spatial filters (local average) in border or inhomogeneous areas, the contribution of each pixel of a given neighborhood of size 3x3, is weighted by its similarity to the corrected pixel. In particular, this similarity weight is the inverse of the Euclidean distance between the spectral signature of the pixels, which is calculated locally using the spectral bands closer to the band presenting the drop-out. It is worth noting that the values of bands with errors are not considered during this process.
The result of this process is similar to a spatial interpolation but taking into account the spectral similarity with neighbors. Although it is a cosmetic correction, it is needed since later processing stages are drastically affected by these anomalous pixel values.

Vertical Striping Correction

The objective of vertical striping correction methods is to estimate the correction factors of each spectral band to correct all the lines of this band. The main assumption consists in considering that both slit and CCD contributions change from one pixel to another (high spatial frequency) in the across-track direction but are constant in the along-track direction, i.e. during the image formation; while surface contribution presents smoother profiles (lower spatial frequencies) in the across-track dimension. Several algorithms already exist to reduce vertical striping, but most of them assume that the imaged surface does not contain structures with spatial frequencies of the same order than noise, which is not always the case. The proposed method introduces a way to exclude the contribution of the spatial high frequencies of the surface from the process of noise removal that is based on the information contained in the spectral domain.
Standard vertical striping reduction approaches take advantage of the constant noise factors in the image columns. Basically, each image's column is averaged resulting in an averaged line (along-track) and then the noise profile is estimated in the across-track direction for each band. By averaging image lines (integrated line profile) the surface contribution is smoothed, the additive random noise is cancelled, and the vertical striping profile remains constant. Consequently, the surface contribution presents lower spatial frequencies in the integrated line profile and can be easily separated from the vertical striping (high frequencies) applying a filter with a suited cut-off frequency.
One of the main drawbacks of these methods is the fact that they do not take into account the possible high frequency components of the surface explicitly. In images presenting structures or patterns in the vertical direction, the averaged profile may present high frequency contributions due to the surface. This will be interpreted as vertical striping, and some columns will be corrected with wrong values, worsening the final image. The proposed correction method is also based on the hypothesis that the vertical disturbance presents higher spatial frequencies than the surface radiance. However, it models the noise pattern by suppressing the surface contribution in the across-track in two different ways: first, avoiding the high frequency changes due to surface edges, and then subtracting the low frequency profile. In addition, thanks to the sequential acquisition of CHRIS of the same scene from five different angles, the robustness of the proposed algorithm can also be improved using together all the multi-angular images of one acquisition. When processing together a higher number of lines, the surface contribution is smoother, and the estimation of the vertical striping is more accurate.

Summary of the Complete Processing Chain

The optimal sequence of algorithms to be applied in order to correct a given image is the following:

  • Drop-outs are detected and corrected.

  • A rough correction of the vertical striping due to the entrance slit is performed. For a given CHRIS image, the estimation of the slit vertical striping is obtained from a previous characterization of the vertical striping pattern stored in a look-up-table (LUT), which includes the dependence on the platform temperature at the given CHRIS acquisition

  • After the preliminary correction of the vertical striping due to the entrance slit, the robust vertical striping correction method is used to estimate directly from the image (or multiangular image set) the remaining vertical striping for each band.

  • Finally, obtained vertical striping coefficients are used to correct the image column values.

 

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