6 November 1998 Limits on computational precision of image compression transformations
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As the development of computational hardware capable of variable precision progresses, the customary requirement of high-precision arithmetic is being relaxed, particularly in automated target recognition applications. Such algorithms typically admit noisy imagery that often has, for example, two to three bits of noise per eight-bit pixel. Since the resulting precision p of five or six bits is nonincreasing throughout the course of a computational cascade, it is reasonable to assume that p equals 8 bits could suffice for most ATR applications. Practical design constraints in addition to noise include limited processor size, weight, and power supply, as well as available computational bandwidth and frame rate. Although limited precision computation can decrease size and power requirement as well as computationally cost, the accrual of computational error can severely compromise resultant accuracy, leading to a design tradeoff between error, computational precision, and speed/power requirements that we call the limited precision problem. In this paper, a restricted instance of the LPP is analyzed, namely, the effect of reduced precision on image compression transforms. Particular emphasis is placed upon the compounding of representational error in the compression process as computation passes through various stages of a given algorithm. Analysis emphasizes effects of noise and computational error on common compression transforms such as visual pattern image coding, vector quantization, and a recently-developed algorithm called. Tests for preservation of input statistics and minimization of mean-squared error (MSE) indicate that, in eight-bit imagery with two to 2.5 bits of noise, as few as five bits of precision suffice for the aforementioned compression algorithms to retain acceptable visual appearance and MSE for ATR operations.
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Mark S. Schmalz, Gerhard X. Ritter, Frank M. Caimi, "Limits on computational precision of image compression transformations", Proc. SPIE 3456, Mathematics of Data/Image Coding, Compression, and Encryption, (6 November 1998); doi: 10.1117/12.330366; https://doi.org/10.1117/12.330366

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