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Model - based approaches to imaging, such as specialized image enhancements in astronomy, facilitate explanations of relationships between observed inputs and computed outputs. These models may be expressed with extended matrix-vector (EMV) algebra, especially when they involve only scalars, vectors, and matrices, and with n-mode or index notations, when they involve multidimensional arrays. also called numeric tensors or, simply, tensors. Although this paper features an example, inspired by exoplanet imaging, that employs tensors to reveal (inverse) 2D fast Fourier transforms in an image enhancement model, the work is actually about the tensor algebra and software, or tensor frameworks, available for model-based imaging. The paper proposes a Ricci-notation tensor (RT) framework, comprising a dual -variant index notation, with Einstein summation convention, and codesigned object-oriented software, called the RTToolbox for MATLAB. Extensions to Ricci notation offer novel representations for entrywise, pagewise, and broadcasting operations popular in EMV frameworks for imaging. Complementing the EMV algebra computable with MATLAB, the RTToolbox demonstrates programmatic and computational efficiency via careful design of numeric tensor and dual-variant index classes. Compared to its closest competitor, also a numeric tensor framework that uses index notation, the RT framework enables superior ways to model imaging problems and, thereby, to develop solutions. [ABSTRACT FROM AUTHOR]

Nonlinear complementary metal-oxide semiconductor (CMOS) image sensors (CISs), such as logarithmic (log) and linear-logarithmic (linlog) sensors, achieve high/wide dynamic ranges in single exposures at video frame rates. As with linear CISs, fixed pattern noise (FPN) correction and salt-and-pepper noise (SPN) filtering are required to achieve high image quality. This paper presents a method to generate digital integrated circuits, suitable for any monotonic nonlinear CIS, to correct FPN in hard real time. It also presents a method to generate digital integrated circuits, suitable for any monochromatic nonlinear CIS, to filter SPN in hard real time. The methods are validated by implementing and testing generated circuits using field-programmable gate array (FPGA) tools from both Xilinx and Altera. Generated circuits are shown to be efficient, in terms of logic elements, memory bits, and power consumption. Scalability of the methods to full high-definition (FHD) video processing is also demonstrated. In particular, FPN correction and SPN filtering of over 140 megapixels per second are feasible, in hard real time, irrespective of the degree of nonlinearity. [ABSTRACT FROM AUTHOR]

An important class of complementary metal-oxide-semiconductor (CMOS) image sensors are those where pixel responses are monotonic nonlinear functions of light stimuli. This class includes various logarithmic architectures, which are easily capable of wide dynamic range imaging, at video rates, but which are vulnerable to image quality issues. To minimize fixed pattern noise (FPN) and maximize photometric accuracy, pixel responses must be calibrated and corrected due to mismatch and process variation during fabrication. Unlike literature approaches, which employ circuit-based models of varying complexity, this paper introduces a novel approach based on low-degree polynomials. Although each pixel may have a highly nonlinear response, an approximately-linear FPN calibration is possible by exploiting the monotonic nature of imaging. Moreover, FPN correction requires only arithmetic, and an optimal fixed-point implementation is readily derived, subject to a user-specified number of bits per pixel. Using a monotonic spline, involving cubic polynomials, photometric calibration is also possible without a circuit-based model, and fixed-point photometric correction requires only a look-up table. The approach is experimentally validated with a logarithmic CMOS image sensor and is compared to a leading approach from the literature. The novel approach proves effective and efficient. [ABSTRACT FROM AUTHOR]