Several recent NASA missions have used the state-of-the-art wavelet-based ICER Progressive Image Compressor
for lossy image compression. In this paper, we describe a methodology for using evolutionary computation to
optimize wavelet and scaling numbers describing reconstruction-only multiresolution analysis (MRA) transforms
that are capable of accepting as input test images compressed by ICER software at a reduced bit rate (e.g., 0.99 bits
per pixel [bpp]), and producing as output images whose average quality, in terms of mean squared error (MSE),
equals that of images produced by ICER’s reconstruction transform when applied to the same test images
compressed at a higher bit rate (e.g., 1.00 bpp). This improvement can be attained without modification to ICER’s
compression, quantization, encoding, decoding, or dequantization algorithms, and with very small modifications to
existing ICER reconstruction filter code. As a result, future NASA missions will be able to transmit greater amounts
of information (i.e., a greater number of images) over channels with equal bandwidth, thus achieving a no-cost
improvement in the science value of those missions.
The research described in this paper uses the CMA-ES evolution strategy to optimize matched forward and inverse
transform pairs for the compression and reconstruction of images transmitted from Mars rovers under conditions subject
to quantization error. Our best transforms outperform the 2/6 wavelet (whose integer variant was used onboard the
rovers), substantially reducing error in reconstructed images without allowing increases in compressed file size. This
result establishes a new state-of-the-art for the lossy compression of images transmitted over the deep-space channel.
The 9/7 wavelet is used for a wide variety of image compression tasks. Recent research, however, has established a
methodology for using evolutionary computation to evolve wavelet and scaling numbers describing transforms that
outperform the 9/7 under lossy conditions, such as those brought about by quantization or thresholding. This paper
describes an investigation into which of three possible approaches to transform evolution produces the most effective
transforms. The first approach uses an evolved forward transform for compression, but performs reconstruction using the
9/7 inverse transform; the second uses the 9/7 forward transform for compression, but performs reconstruction using an
evolved inverse transform; the third uses simultaneously evolved forward and inverse transforms for compression and
reconstruction. Three image sets are independently used for training: digital photographs, fingerprints, and satellite
images. Results strongly suggest that it is impossible for evolved transforms to substantially improve upon the
performance of the 9/7 without evolving the inverse transform.
Wavelets provide an attractive method for efficient image compression. For transmission across noisy or bandwidth
limited channels, a signal may be subjected to quantization in which the signal is transcribed onto a
reduced alphabet in order to save bandwidth. Unfortunately, the performance of the discrete wavelet transform
(DWT) degrades at increasing levels of quantization. In recent years, evolutionary algorithms (EAs) have been
employed to optimize wavelet-inspired transform filters to improve compression performance in the presence of
quantization. Wavelet filters consist of a pair of real-valued coefficient sets; one set represents the compression
filter while the other set defines the image reconstruction filter. The reconstruction filter is defined as the
biorthogonal inverse of the compression filter. Previous research focused upon two approaches to filter optimization.
In one approach, the original wavelet filter is used for image compression while the reconstruction
filter is evolved by an EA. In the second approach, both the compression and reconstruction filters are evolved.
In both cases, the filters are not biorthogonally related to one another. We propose a novel approach to filter
evolution. The EA optimizes a compression filter. Rather than using a wavelet filter or evolving a second filter
for reconstruction, the reconstruction filter is computed as the biorthogonal inverse of the evolved compression
filter. The resulting filter pair retains some of the mathematical properties of wavelets. This paper compares
this new approach to existing filter optimization approaches to determine its suitability for the optimization of
image filters appropriate for defense applications of image processing.
State-of-the-art image compression and reconstruction schemes utilize wavelets. Quantization and thresholding are
commonly used to achieve additional compression, but cause permanent, irreversible information loss. This paper
describes an investigation into whether evolutionary computation (EC) may be used to optimize forward
(compression-only) transforms capable of matching or exceeding the compression capabilities of a selected wavelet,
while reducing the aggregate error in images subsequently reconstructed by that wavelet. Transforms are
independently trained and tested using three sets of images: digital photographs, fingerprints, and satellite images.
Many image processing algorithms utilize the discrete wavelet transform (DWT) to provide efficient compression
and near-perfect reconstruction of image data. Defense applications often require the transmission of data at
high levels of compression over noisy channels. In recent years, evolutionary algorithms (EAs) have been utilized
to optimize image transform filters that outperform standard wavelets for bandwidth-constrained compression
of satellite images. The optimization of these filters requires the use of training images appropriately chosen for
the image processing system's intended applications. This paper presents two robust sets of fifty images each
intended for the training and validation of satellite and unmanned aerial vehicle (UAV) reconnaissance image
processing algorithms. Each set consists of a diverse range of subjects consisting of cities, airports, military
bases, and landmarks representative of the types of images that may be captured during reconnaissance missions.
Optimized algorithms may be "overtrained" for a specific problem instance and thus exhibit poor performance
over a general set of data. To reduce the risk of overtraining an image filter, we evaluate the suitability of each
image as a training image. After evolving filters using each image, we assess the average compression performance
of each filter across the entire set of images. We thus identify a small subset of images from each set that provide
strong performance as training images for the image transform optimization problem. These images will also
provide a suitable platform for the development of other algorithms for defense applications. The images are
available upon request from the contact author.
Evolutionary algorithms (EAs) have been employed in recent years in the design of robust image transforms.
EAs attempt to improve the defining filter coefficients of a discrete wavelet transform (DWT) to improve image
quality for bandwidth-restricted surveillance applications, such as the transmission of images by swarms of
unmanned aerial vehicles (UAVs) over shared channels. Regardless of the specific algorithm employed, filter
coefficients are optimized over a common fitness landscape that defines allowable configurations that filters may
take. Any optimization algorithm attempts to identify highly-fit filter configurations within the landscape. The
evolvability of transform filters depends upon the ruggedness, deceptiveness, neutrality, and modality of the
underlying landscape traversed by the EA. We have previously studied the evolvability of image transforms for
satellite image processing with regards to ruggedness and deceptiveness. Here we examine the position of wavelet
coefficients within a landscape to determine whether optimization algorithms should be seeded near this position
or randomly seeded in the global landscape. Through examination of landscape deceptiveness, both near wavelet
coefficients and throughout the global range of the landscape, we determine that the neighborhood surrounding
the wavelet contains a greater concentration of highly fit solutions. EAs that concentrate their search effort in
this neighborhood have a better chance of identifying filters that improve upon standard wavelets. An improved
understanding of the underlying fitness landscape characteristics impacts the design of evolutionary algorithms
capable of identifying near-optimal image transforms suitable for deployment in defense and security applications
of image processing.
This paper describes the automatic discovery, via an Evolution Strategy with Covariance Matrix Adaptation (CMA-ES),
of vectors of real-valued coefficients representing matched forward and inverse transforms that outperform the
9/7 Cohen-Daubechies-Feauveau (CDF) discrete wavelet transform (DWT) for satellite image compression and
reconstruction under conditions subject to quantization error. The best transform evolved during this study reduces
the mean squared error (MSE) present in reconstructed satellite images by an average of 33.78% (1.79 dB), while
maintaining the average information entropy (IE) of compressed images at 99.57% in comparison to the wavelet. In
addition, this evolved transform achieves 49.88% (3.00 dB) average MSE reduction when tested on 80 images from
the FBI fingerprint test set, and 42.35% (2.39 dB) average MSE reduction when tested on a set of 18 digital
photographs, while achieving average IE of 104.36% and 100.08%, respectively. These results indicate that our
evolved transform greatly improves the quality of reconstructed images without substantial loss of compression
capability over a broad range of image classes.
A wide variety of signal and image processing applications, including the US Federal Bureau of Investigation's fingerprint compression standard  and the JPEG-2000 image compression standard , utilize wavelets. This paper describes new research that demonstrates how a genetic algorithm (GA) may be used to evolve transforms that outperform wavelets for satellite image compression and reconstruction under conditions subject to quantization error. The new approach builds upon prior work by simultaneously evolving real-valued coefficients representing matched forward and inverse transform pairs at each of three levels of a multi-resolution analysis (MRA) transform. The training data for this investigation consists of actual satellite photographs of strategic urban areas. Test results show that a dramatic reduction in the error present in reconstructed satellite images may be achieved without sacrificing the compression capabilities of the forward transform. The transforms evolved during this research outperform previous start-of-the-art solutions, which optimized coefficients for the reconstruction transform only. These transforms also outperform wavelets, reducing error by more than 0.76 dB at a quantization level of 64. In addition, transforms trained using representative satellite images do not perform quite as well when subsequently tested against images from other classes (such as fingerprints or portraits). This result suggests that the GA developed for this research is automatically learning to exploit specific attributes common to the class of images represented in the training population.
Military imaging systems often require the transmission of copious amounts of data in noisy or bandwidth-limited
situations. High rates of lossy image compression may be achieved through the use of quantization at the expense
of resulting image quality. We employ genetic algorithms (GAs) to evolve military-grade transforms capable
of improving reconstruction of satellite reconnaissance images under conditions subject to high quantization
error. The resulting transforms outperform existing wavelet transforms at a given compression ratio allowing
transmission of data at a lower bandwidth. Because GAs are notoriously difficult to tune, the selection of
appropriate variation operators is critical when designing GAs for military-grade algorithm development. We
test several state-of-the-art real-coded crossover and mutation operators to develop an evolutionary system
capable of producing transforms providing robust performance over a set of fifty satellite images of military
interest. With appropriate operators, evolved filters consistently provide an average mean squared error (MSE)
reduction greater than 17% over the original wavelet transform. By improving image quality, evolved transforms
increase the amount of intelligence that may be obtained reconstructed images.
State-of-the-art signal compression and reconstruction techniques utilize wavelets. However, recently published
research demonstrated that a genetic algorithm (GA) is capable of evolving non-wavelet inverse transforms that
consistently outperform wavelets when used to reconstruct one- and two-dimensional signals under conditions subject
to quantization error. This paper summarizes the results of a series of three follow-on experiments. First, a GA is
developed to evolve matched forward and inverse transform pairs that simultaneously minimize the compressed file size
(FS) and the squared error (SE) in the reconstructed file. Second, this GA is extended to evolve a single set of
coefficients that may be used at every level of a multi-resolution analysis (MRA) transform. Third, this GA is expanded
to achieve additional SE reduction by evolving a different set of coefficients for each level of an MRA transform. Test
results indicate that coefficients evolved against a single representative training image generalize to effectively reduce
SE for a broad class of reconstructed images.