An image sensor system-level pixel-to-pixel photo-response non-uniformity (PRNU) error tolerance method is presented
in this paper. A scheme is developed to determine sensor PRNU acceptability and corresponding sensor application
categorization. Many low-cost imaging systems utilize CMOS imagers with integrated on-chip digital logic for
performing image processing and compression. Due to pixel geometry and substrate material variations, the light
sensitivity of pixels will be non-uniform (PRNU). Excessive variation in the sensitivity of pixels is a significant cause of
the screening rejection for these image sensors. The proposed testing methods in this paper use the concept of
acceptable degradation applied to the camera system processed and decoded images of these sensors. The analysis
techniques developed in this paper give an estimation of the impact of the sensor's PRNU on image quality. This
provides the ability to classify the sensors for different applications based upon their PRNU distortion and error rates.
The human perceptual criteria is used in the determination of acceptable sensor PRNU limits. These PRNU thresholds
are a function of the camera system's image processing (including compression) and sensor noise sources. We use a
Monte Carlo simulation solution and a probability model-based simulation solution along with the sensor models to
determine PRNU error rates and significances for a range of sensor operating conditions (e.g., conversion gain settings,
integration times). We develop correlations between industry standard PRNU measurements and final processed and
decoded image quality thresholds. The results presented in this paper show that the proposed PRNU testing method can
reduce the rejection rate of CMOS sensors. Comparisons are presented on the sensor PRNU failure rates using industry
standard testing methods and our proposed methods.
A simple multi-channel imager restoration method is presented in this paper. A method is developed to correct channel
dependent cross-talk of a Bayer color filter array sensor with signal-dependent additive noise. We develop separate cost
functions (weakened optimization) for each color channel-to-color channel component. Regularization is applied to each
color component, instead of the standard per color channel basis. This separation of color components allows us to
calculate regularization parameters that take advantage of the differing magnitudes of each color component cross-talk
blurring. Due to a large variation in the amount of blurring for each color component, this separation can result in an
improved trade-off between inverse filtering and noise smoothing. The restoration solution has its regularization
parameters determined by maximizing the developed local pixel SNR estimations (HVS detection constraint). Local
pixel adaptivity is applied. The total error in the corrected signal estimate (from bias error and amplified noise variance)
is used in the local pixel SNR estimates. Sensor characterization a priori information is utilized. The method is geared
towards implementation into the on-chip digital logic of low-cost CMOS sensors. Performance data of the proposed
correction method is presented using color images captured from low cost embedded imaging CMOS sensors.
A pixel signal cross-talk correction method that utilizes knowledge of a color image sensor's performance characteristics is presented. The objective is to create a simple, non-iterative algorithm that can be implemented in the on-chip digital logic of an imaging sensor. Inverse cross-talk Bayer color filter array pattern filters are determined for the blurring, multi-channel, cross-channel problem. Simple noise and cross-talk models are developed and used to solve for the corrective deconvolution filters. The noise statistics used have both signal independent and dependent components, and include the noise associated with cross-talk. The methodology is independent of image statistics. The inverse filters are found by solving a set of simultaneous linear equations in the discrete Fourier frequency domain. A direct deterministic regularization method with constrained least squares is then used to solve the ill-posed problem. The local pixel blurred signal-to-noise ratio is used as the regularization parameter. This yields an inverse blur filter weighted by a local scalar noise filter. The resulting method provides a locally adaptive trade-off between cross-talk correction and noise smoothing. Algorithm performance is compared with the standard 3x3 matrix color correction method for image mean square error, color error, flat SNR, and modulation transfer function.
In the conversion of an imager’s pixel data from electrons to digital numbers, a scalar quantization is performed. For CMOS sensors used in consumer applications, this scalar quantization is usually performed by an on-chip analog-to-digital converter (ADC) preceded by an amplifier. It is desired that the scalar quantization operation minimize the error between the analog input signal and the quantized output. One approach is to use a non-uniform quantizer for a signal with a known probability density function to minimize the mean square error. The Lloyd-Max algorithm can be used to determine the optimal quantization intervals and reconstruction levels. However, a probability model for the variations of pixels in a sensor is difficult to determine since the sensor can receive a vast number of greatly differing image data. Additionally, a quantizer with non-uniform intervals is difficult to implement, can be unstable, and has limited flexibility. Thus, it is preferred to use a simple linear, uniform quantization step size ADC to sample the sensor’s data.
The approach taken in this paper is to develop a scalar quantizer that utilizes knowledge of a sensor’s performance characteristics. The decision and reconstruction levels of a non-uniform quantizer are determined from the noise versus signal characteristics of the sensor. A linear, uniform quantization step size ADC can be used to 'over-encode’ (sample using more bits per pixel than required) the sensor’s data. The number of bits per pixel can then be reduced using a sensor characterization optimized mapping to a lower bit depth. This results in a reduction of the sensor’s digitized data.
The conversion function from pixel electrons to the digitized signal value is developed in this paper for a CMOS sensor with small pixel size designed for embedded applications. These sensors will typically exhibit lower signal to noise ratios due to their lower well capacity (lower dynamic range), higher levels of random noise, and higher cross-talk (the loss of photons or electrons from a pixel to neighboring pixels); which makes them ideal for this type of mapping. The performance of the proposed noise-based quantization method is measured through the calculation of mean square errors and relative compressibility of quantized sample images.
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