Hiroyuki Takeda (University of California, Santa Cruz), Sina Farsiu (University of California), Julian Christou (University of California), Peyman Milanfar (University of California)
Keywords: Imaging
Abstract:
The drizzle algorithm is a widely used tool for image enhancement in the astronomical literature. For example a very popular implementation of this method, as studied by Frutcher and Hook [2001], has been used to fuse, denoise, and increase the spatial resolution of the images captured by the Hubble Space Telescope. However, the drizzle algorithm is an ad-hoc method, equivalent to an adaptive linear filter, insensitive to the (pixel) values of data, which limits its performance.
To improve the performance of the drizzle algorithm, we make contact with the field of non-parametric statistics and generalize the tools and results for use in image processing and reconstruction. In contrast to the parametric methods, which rely on a specific model of the signal of interest, non-parametric methods rely on the data itself to dictate the structure of the model, in which case this implicit model is referred to as a regression function. We promote the use and improve upon a class of non-parametric methods called kernel regression.
In this paper, we introduce new aspects of the Kernel Regression to the astronomy science community. The novelties of this paper include
1. 1. We exploit the kernel regression framework to justify a powerful variation of the drizzle algorithm with superior performance, applicable to both regularly and irregularly sampled data.
2. Unlike the drizzle algorithm, the effective size and shape of the kernel (window) in the proposed method are adapted locally not only to the spatial sampling density of the data, but also to the actual (measured pixel) values of those samples. Such novel data-adaptive implementation of the drizzle algorithm is especially suitable for reconstructing images with sharp edges
3. The proposed method is applicable to both single frame and multi-frame processing scenarios, and is equally effective for both oversampled and undersampled images.
4. The proposed method takes advantage of a generic model that is optimal for reconstructing images contaminated with different noise models, including additive Gaussian, Laplacian, and Salt & Pepper.
Experiments on simulated and real data show diverse applications and the superiority of the proposed adaptive technique with respect to the state of the art methods in the literature (including the drizzle algorithm, the bilateral filter and wavelet-based methods). We show that the proposed algorithm not only visually and numerically (Peak Signal to Noise Ratio comparison) improves the quality of reconstruction, but also due to its non-parametric structure will result in images that are faithful with respect to the photometric properties of the original (ideal) image.
Date of Conference: September 10-14, 2006
Track: Imaging