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Reconstruction of Multispatial, Multispectral Image Data Using Spatial Frequency Content

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Reconstruction of Multispatial, Multispectral Image Data Using Spatial Frequency Content R. A. SCHOWENGERDT* Office of Arid Lands Studies and Systems and Zndustrial Engineering Department University of Arizona Tucson, AZ 8571 9 Reconstruction of Multispatial, MuItispectraI Image Data Using Spatial Frequency Content Multispatial, multispectral imagery is reconstructed by computer processing to enhance information extraction. recent interest and success with simpler ap- proaches (Hung, 1979). HERE HAS BEEN considerable interest in tech- It has been suggested (Colvocoresses, 1977) that Tniques for reducing the quantity of image data a mixture of high spatial resolution spectral bands transmitted from spacecraft to ground receiving and lower resolution bands may be an acceptable stations. The concern about excessive data way to reduce data rates without sacrificing image acquisition/transmission rates is particularly im- information content. The basis for this suggestion portant for the next generation of high spatial and is that only one or two spectral bands are required radiometric resolution sensors, such as the the- to define the majority of edges in a scene, and matic mapper (TM) on Landsat D, the multispectral hence only these bands need to be of high resolu- resource sampler (MRS),SPOT (Chevrel, 1979), and tion. A significant advantage of mixed resolution, Mapsat (Colvocoresses, 1979). or what may be termed multispatial, compression Techniques that reduce data quantity must also is that it can be accomplished by appropriate ABSTRACT:A data compression technique that utilizes a mixture of spatial res- olutions (multispatial) for a multispectral scanner is described. The com- plementary reconstruction procedure that extrapolates edge information from the high resolution banqs) to the low resolution bands is also discussed. Exam- ples of Landsat MSS imagery that have been compressed and reconstructed to the original resolution are presented. Error rates are calculated for two types of scenes, one containing prominent topographic effects, the other of an agricul- tural area. Zmprooement in radiometric quality of up to 40 percent is achieved by application of the reconstruction procedure to the compressed data. preserve image radiometry, resolution, and geom- specification of the sensor's instantaneous-field- etry within acceptable limits. A two-stage process of-view. (IFOV) and hence requires no on-board is therefore indicated, the first stage being data data processing. Multispatial sensors are already compression and the second being data recon- fairly common, examples being the combination of struction. A large amount of research has been return beam vidicon (~~v)lmultispectralscanner done on this general problem (Pratt, 1976; Pratt, (MSS) on Landsat 3 and the thematic mapper 1978) and on satellite imagery in particular (Gon- (TM)/MSSplanned for Landsat D (Table 1). The zalez and Wintz, 1977). Much of this work has de- variable resolutions of these systems result, how- scribed complex transform techniques that have ever, not from data compression considerations, found little operational application, but there is but rather from the detector signal-to-noise ratio characteristics and manufacturing constraints. * This work was performed, in part, as an employee This paper describes a relatively simple recon- of the U.S. Geological Survey, Reston, Virginia. struction technique for multispatial imagery. The PHOTOCR.~MMETRICENGINEERING AND REMOTE SENSING, Vol. 46, No. 10, October 1980, pp. 1325-1334. PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1980 Instantaneous field-of-view Satellite Sensor Spectral bands IFOV (m) Landsat 3 MSS visible, near IR 80 thermal IR 240 RBV visible 25 Landsat D TM visible, near IR 30 thermal IR 120 MSS visible, near 1d 801240 thermal rR SPOT Linear visible, near IR 20 may panchromatic 10 Mapsat Linear blue-green (proposed) array red near IR technique utilizes computer processing to par- The same arguments for an area of flat topogra- tially restore edge sharpness lost in the low- phy that contains human activities, such as ag- resolution imagery. It is applicable not only to the riculture or urbanization, are not necessarily valid. quantitative reconstruction of compressed data, However, it is apparent that many edges, such as but also to the enhancement of color composites of those between agricultural fields or roads and sur- multispatial imagery. Digital composites of Land- rounding vegetation or soil, will exist, at varying sat 3 RBV and ~ssimagery are one current example contrast, in all the spectral bands. The problem of this application (Gehring and Peny, 1979). here is' that these edges are color edges and the information that defines them changes from band to band. For example, the contrast of the edge may Edges in many natural scenes are caused by to- completely reverse polarity as seen in the Landsat pography, e.g., shadows. Since these boundaries image of agriculture in Figure 4. An approach is occur in all bands of a multispectral image, it is developed later to deal with this more complex reasonable to assume that the high spatial fre- situation. quency components (those contributing to edge sharpness) of such images are consistently corre- lated between spectral bands. The lower fre- A simulation of multispatial, multispectral im- quency components will carry much of the spec- agery was made with the Landsat images of Fig- tral (color) information and hence will show a ures 1 and 4. Reconstruction of the low resolution greater variability of correlation between spectral data was then performed with the techniques de- bands. This situation is verified by analysis of a scribed below. portion of a Landsat scene of the Grand Canyon (Figure la). A low-pass image, created by spatial SIMULATION OF COMPRESSED, filtering of the original with a 3-by-3 pixel av- MULTISPATIAL IMAGERY eraging filter (Figure lb), and a high-pass image, Band 5 (red) was retained at its original resolu- obtained by subtracting the low-pass image from tion of 80-by-80 m and bands 4, 6, and 7 were the original (Figure lc), were calculated for each reduced to 240-by-240 m resolution by a 3-by-3 spectral band. The two-dimensional histogram pixel low-pass filter (Figure lb). These data were between low and high-pass images of several then resampled at 240 m to represent the data as spectral bands was calculated, examples of which acquired by a mixed resolution sensor. The quan- are shown in Figure 2. A linear regression was tity of data in bands 4, 6, and 7 is, therefore, re- then applied to the histograms to determine the duced to one-ninth that of the original imagery. degree of fit to a straight line. The results (Figure This step of the process is depicted in Figure 5. 3) support the supposition that, for scenes with The bottom image in Figure 5 represents the data topographic relief, edges correlate more consis- transmitted to the ground for bands 4, 6, and 7, tently from band to band than does low frequency along with the high resolution band 5 (similar to information. Note that for uncorrelated bands, the upper image of Figure 5). Experience has edges possess a greater degree of correlation than shown that band 5 generally has more scene con- do low frequencies, and for correlated bands the trast than the other bands, making it the logical opposite is true. choice for the high resolution band. RECONSTRUCTION OF MULTISPATIALIMULTISPECTRAL IMAGE DATA H I STOGRAH i I NO FILTER ! kO GRAY LEVEL (A) Original (b) Low pass FILTER (c) High pass FIG.1. Examples of low and high pass images and their gray level histograms. GRAY LEVEL- BAMO 4 7 HIGH FREQUENCIES ' 1 ' FIG.2. Correlation histograms between bands for low and high frequency com- ponents (Landsat ID X2478-17205). PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1980 ORIGINAL I I I I I 0.7 1 4-5 6-7 5-6 4-7 5-7 CORRELATED BANDS UNCORREUTED MNDS FIG.3. Degree of correlation between bands for low LOW PASS (.) and high (+) frequency components (Landsat ID #247817205). 1 Although the resolutions simulated with these Landsat data are a factor of three or four lower than anticipated with the TM or MRS,the comparative results obtained in this study should remain valid at higher resolutions. RECONSTRUCTION OF COMPRESSED IMAGES This section describes ground-based computer processing to restore the resolution lost in the Eompressed data. The first step is to resample the RESAMPLED imagery at the higher sampling rate of band 5. This is accomplished by some type of interpolation, such as nearest-neighbor, bilinear, or cubic spline (Bernstein, 1976). Examples of each are shown in Figure 6. Nearest-neighbor interpolation amounts in this case to replication of pixels and lines, and the image exhibits characteristic blockiness. Bilinear and cubic spline interpolation yield more FIG.5. Simulation of compressed data from Landsat realistic images, with cubic spline interpolation image. producing a slightly sharper enlargement. Several types of interpolation have been compared for BAND 5 BAND 7 -geometric correction of Landsat data (Simon, 1975; Shlien, 1979) and cubic spline has been shown to be a good compromise between error rate and computational cost. It is also the tech- nique used at the EROS Data Center for produc- tion of enhanced Landsat products (Holkenbrink, 1978). At this point, it is instructive to note that the goal of the interpolation process is to reproduce as closely as possible a low-pass filtered image (Fig- ure lb), as if the data have not been resampled to achieve compression. This is clear from the type of edge restoration described below. The three types of interpolation are compared for the Grand Can- yon image in terms of this criterion in Table 2. Bilinear interpolation is an improvement over nearest-neighbor by about 10 percent, while cubic spline results in only a small additional improve- ment. The disappointing performance of the cubic spline algorithm in this case can be explained by FIG.4.
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