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This paper gives a brief survey of the design of masks for Hadamard spectrometers and image scanners. Three different criteria are described for judging a mask, as well as techniques for choosing masks that are not too far from the optimum.
The IRMOS (infrared multiobject spectrometer) is an imaging dispersive spectrometer, with a micromirror array to select desired objects. In standard operation, the mirrors are "opened" in patterns such that the resulting spectra do not overlap on the detector. The IRMOS can also be operated in a Hadamard mode, in which the spectra are allowed to overlap, but are modulated by opening the mirrors in many combinations. This mode enables the entire field of view to be observed with the same sensitivity as in the standard mode if the uncertainty is dominated by the detector read noise. We explain the concept and discuss the benefits with an example observation of the Orion Trapezium using the 2.1 m telescope at Kitt Peak National Observatory.
Computational algorithm for fast Hadamard matrix transform of order 12 via factorization
A set of compressed, then reconstructed, test images submitted to the Comet Rendezvous Asteroid Flyby (CRAF)/Cassini project is presented as part of its evaluation of near lossless high compression algorithms for representing image data. A total of seven test image files were provided by the project. The seven test images were compressed, then reconstructed with high quality (root mean square error of approximately one or two gray levels on an 8 bit gray scale), using discrete cosine transforms or Hadamard transforms and efficient entropy coders. The resulting compression ratios varied from about 2:1 to about 10:1, depending on the activity or randomness in the source image. This was accomplished without any special effort to optimize the quantizer or to introduce special postprocessing to filter the reconstruction errors. A more complete set of measurements, showing the relative performance of the compression algorithms over a wide range of compression ratios and reconstruction errors, shows that additional compression is possible at a small sacrifice in fidelity.
Five coding techniques in the spatial and transform domains have been evaluated for SAR image compression: linear three-point predictor (LTPP), block truncation coding (BTC), microadaptive picture sequencing (MAPS), adaptive discrete cosine transform (ADCT), and adaptive Hadamard transform (AHT). These techniques have been tested with Seasat data. Both LTPP and BTC spatial domain coding techniques provide very good performance at rates of 1-2 bits/pixel. The two transform techniques, ADCT and AHT, demonstrate the capability to compress the SAR imagery to less than 0.5 bits/pixel without visible artifacts. Tradeoffs such as the rate distortion performance, the computational complexity, the algorithm flexibility, and the controllability of compression ratios are also discussed.
A method of improving the compression of image data using Lempel-Ziv-based coding is presented. Image data is first processed with a simple transform, such as the Walsh Hadamard Transform, to produce subbands. The subbanded data can be rounded to eight bits or it can be quantized for higher compression at the cost of some reduction in the quality of the reconstructed image. The data is then run-length coded to take advantage of the large runs of zeros produced by quantization. Compression results are presented and contrasted with a subband compression method using quantization followed by run-length coding and Huffman coding. The Lempel-Ziv-based coding in conjunction with run-length coding produces the best compression results at the same reconstruction quality (compared with the Huffman-based coding) on the image data used.
Rate distortion functions for two-dimensional homogeneous isotropic images are compared with the performance of 5 source encoders designed for such images. Both unweighted and frequency weighted mean square error distortion measures are considered. The coders considered are differential PCM (DPCM) using six previous samples in the prediction, herein called 6 pel (picutre element) DPCM; simple DPCM using single sample prediction; 6 pel DPCM followed by entropy coding; 8 x 8 discrete cosine transform coder, and 4 x 4 Hadamard transform coder. Other transform coders were studied and found to have about the same performance as the two transform coders above. With the mean square error distortion measure DPCM with entropy coding performed best. The relative performance of the coders changes slightly when the distortion measure is frequency weighted mean square error. The performance of all the coders was separated by only about 4 dB.
Fourier and Hadamard transformation codings for multidimensional data channel noise immunity and bandwidth reduction
The two-dimensional transform used in the research TV source encoder, RM2 is discussed. It is shown that both conceptually and in terms of the number of required computations, the RM2 transform is considerably simpler than the Fast Hadamard Transform. The latter can in fact be generated by extending the RM2 transform.
A fast sequency-ordered Walsh transform algorithm is presented; this sequency-ordered fast transform is complementary to the sequency-ordered fast Walsh transform introduced by Manz (1972) and eliminating gray code reordering through a modification of the basic fast Hadamard transform structure. The new algorithm retains the advantages of its complement (it is in place and is its own inverse), while differing in having a decimation-in time structure, accepting data in normal order, and returning the coefficients in bit-reversed sequency order. Applications include estimation of Walsh power spectra for a random process, sequency filtering and computing logical autocorrelations, and selective bit reversing.
This semi-tutorial paper describes the process of using orthogonal transforms for the purposes of encoding TV picture data. Results pertaining to a 6:1 data compression experiment using the Walsh-Hadamard transform are included.
A channel separation algorithm for the frequency division multiple access/time division multiplexing (FDMA/TDM) scheme is presented. It is shown that implementation using this algorithm can be more effective than the fast Fourier transform (FFT) algorithm when only a small number of carriers need to be selected from many, such as satellite Earth terminals. The algorithm is based on polyphase filtering followed by application of a generalized Walsh-Hadamard transform (GWHT). Comparison of the transform technique used in this algorithm with discrete Fourier transform (DFT) and FFT is given. Estimates of the computational rates and power requirements to implement this system are also given.
Hadamard transform source encoding application to Apollo unified S-band telemetry links, considering possible system performance improvement
The Earth Resources Technology Satellite system is studied, with emphasis on sensors, data processing requirements, and image data compression using the Fast Fourier and Hadamard transforms. The ERTS-A system and the fundamentals of remote sensing are discussed. Three user applications (forestry, crops, and rangelands) are selected and their spectral signatures are described. It is shown that additional sensors are needed for rangeland management. An on-board information processing system is recommended to reduce the amount of data transmitted.
The following techniques are considered for classifying low resolution satellite imagery: (1) Gradient operations; (2) histogram methods; (3) gray level detection; (4) frequency domain operations; (5) Hadamard transform in digital image matching; and (6) edge and line detection schemes.
The author has identified the following significant results. The annotation system produced a RMSE of about 200 m ground distance in the MSS data system with the control data used. All the analytical MSS interpretation models tried were highly significant. However, the gains in forest sampling efficiency that can be achieved by using the models vary from zero to over 50 percent depending on the area to which they are applied and the sampling method used. Among the sampling methods tried, regression sampling yielded substantial and the most consistent gains. The single most significant variable in the interpretation model was the difference between bands 5 and 7. The contrast variable, computed by the Hadamard transform was significant but did not contribute much to the interpretation model. Forest areas containing very large timber volumes because of large tree sizes were not separable from areas of similar crown cover but containing smaller trees using ERTS image interpretation only. All correlations between space derived timber volume predictions and estimates obtained from aerial and ground sampling were relatively low but significant and stable. There was a much stronger relationship between variables derived from MSS and U2 data than between U2 and ground data.
Techniques of video compression applicable to remotely piloted vehicles (RPVs) are investigated. One approach is to reduce the frame rate, the other is to reduce the number of bits per sample needed to represent static picture detail by means of digital video compression. Hadamard transforms of 8 x 8 subpictures, with adaptive and nonadaptive quantization of transform coefficients, were investigated for the latter technique. Tapes of typical RPV video, processed by Aeronautronic Ford to simulate four frame rates, were again processed by the Ames real-time video system to obtain a variety of compressions of each of the four frame rates.
Image data are compressed for transmission by simple, economical circuitry. Compressor handles data in blocks of 64 samples. Mean from previous line is subtracted, and pseudo-random sequence of positive and negative 1's multiplies samples of each block. Hadamard transform applied to blocks yields 64 transform coefficients. Each coefficient is compared with approximation to corresponding coefficient of previous line, and difference is quantized. Values are transmitted or stored. Procedure is reversed to reproduce image.