KEYWORDS: Image restoration, Point spread functions, Principal component analysis, Process modeling, Image processing, Image quality, Image analysis, Algorithms, Signal to noise ratio, Statistical analysis
Approaches analyzing local characteristics of an image prevail in image restoration. However, they are less effective in cases of restoring images degraded by large size point spread functions (PSFs) and heavy noise. In this paper, we propose a set theoretic approach to object-based image restoration that involves the following issues: representing the common characteristics of a class of objects that images of interest contain, the formulation to combine prior knowledge of the object, and the algorithm to find the solution. The common characteristics of objects are represented as deterministic sets built on principal component analysis based models of objects. Combining these sets with those arising from observed data, object-based image restoration is formulated in a set theoretic framework. Finally, a parallel subgradient projection algorithm is applied to find the intersection of the sets. Experiments performed on frontal face images using the proposed approach show significant improvement in large size and heavy noise degradation, compared with traditional methods based on local analysis. The proposed approach opens the possibilities of introducing the more prior knowledge pertaining to objects in terms of deterministic sets and solving the problem by abundant numerical algorithms under set theoretic framework.
A hybrid method for image interpolation is proposed. The method consists of three different approaches: Circular arc or B-spline interpolation, linear interpolatino and human visual sensitivity based on interpolation. The image can be divided into three regions: linear smooth region, sharp edge region and human visual insensitive region. The method uses local variance and mean value to find different regions adaptively. The linear interpolation is used for linear smooth region. The human visual sensitivity based interpolation is used for human visual insensitive region and the circular arc or B-spline interpolation is used for sharp edge region. Experiments show that proposed method produces results that are more visually realistic than standard function-fitting methods.
KEYWORDS: Interference (communication), Brain, Reconstruction algorithms, Signal to noise ratio, Electroencephalography, Filtering (signal processing), Wavelets, Silicon, Adaptive optics, Chemical elements
Event-related potential (ERP) plays a very important role in the field of human brain activities research. It is a practical method for measuring the brain functions. By now, the traditional methods remained in extracting of ERP are that rely on accumulative averaging techniques, which getting in a totally averaging result. In practice, however, it is obviously that the ERPs are not identical with each other in response for a number of repeated stimuli, neither in signal pattern nor response time. So that extracting ERP from a single trial is the goal of investigators in pursuit of. That is a different task, although some worthy works had been reported. A novel method is presented in this paper, which can extract single trial ERP by means of higher order cumulant (HOC) followed by cepstrum technique. Based on the theory of HOC, it can deal with additive noise very well, regardless the noise is white or not. For a single-trial ERP signal measured in strong background noise, the complex cepstrum of higher order cumulants of the signal is calculated firstly, and then the original ERP is reconstructed. The experiment shows that this method has a better performance in reconstructing single-trial ERP in the case of lower signal to noise ratio.
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