Examples of constrained iterative restoration of SPOT panchromatic images, with prefiltering for noise reduction

In this project, image blur was reduced in SPOT HRV panchromatic band images by using iterative restoration techniques with modifications to suppress noise amplification. In the limit, as the iterations continue the restoration process converges to inverse filtering and thus is subject to excessive noise amplification. One method of reducing noise effects is to limit the iterations while achieving partial blur reduction; another is to suppress noise in the degraded image before restoration by preprocessing both the degraded image and the sensor system point spread function with a noise smoothing filter. A variation of the latter technique was used in this work. Instead of a smoothing filter, a smoothing and interpolating filter was applied, which also expanded the image size. Examples of iterative restoration, with a positive constraint to reduce ringing artifacts for both original size and enlarged size images, use simulated data and SPOT panchromatic spectral band, 10-m ground sample distance images. In this study, processing was terminated when the image, observed on a computer display monitor, was determined to have reasonable deblurring and tolerable noise amplification. In effect, this interactive technique falls between high spatial frequency enhancement for partial blur reduction and, in the limiting case, inverse filter restoration. 1 Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government. INTRODUCTION The goal of image restoration is to recover the original scene from degraded observations using techniques oriented toward modeling the degradation, blur, and noise and applying an inverse procedure to obtain an approximation of the original scene (Katsaggelos, 1991). This report describes examples of image blur reduction by means of iterative inverse filtering for restoration. An advantage of this technique is that only a model of the blur degradation is needed; no noise model is required. This report follows a previous report (Lemeshewsky, 1993) that described blur reduction in SPOT panchromatic images and a technique to estimate the point spread function (PSF), which is the imaging system's impulse response or blur function. In the limit as the number of iterations approaches infinity, the process converges to inverse filtering and gives excessive noise amplification. In some cases, depending on the degree of blur and noise degradations, reasonable blur reduction can be achieved without objectionable noise levels by limiting the iterations (Lim, 1990). Although noise amplification is a consequence of iterative inverse filtering, there are additional reported techniques (Schafer and others 1981; Kawata and Ichioka, 1980a) that mitigate noise effects. Two techniques are to apply constraints to the restoration solution or to first reduce the noise of the degraded image. The latter can be achieved by preprocessing the degraded image with a low-pass, noise smoothing filter; however, this additional smoothing (that is, blur) must be included in the degradation model. Schafer and others (1981) described the restoration of twodimensional signals, not images, by applying a smoothing and interpolating filter to both the degraded signal and the impulse response of the degradation model before restoration. Also, they found that constraints imposed on the iterative solution would reduce ringing and other artifacts. Application of these techniques to images is reported herein. This report describes tests and gives examples of image blur reduction in which the degraded image was first preprocessed by a noise smoothing-interpolation (SI) technique to reduce noise amplification. Also the iterations were limited, and a positive constraint was applied to the iterative solution to suppress negative intensities caused by ringing and noise amplification. Restoration examples are given for simulated data and SPOT panchromatic band 10-m pixel images. The report is organized into five sections. Section I briefly describes the noise amplification problem associated with inverse filter restoration. Section II describes the minor modification required in the iterative inverse filter process in order to use the SI technique for noise reduction. Section III gives examples of blur reduction for a simple, simulated image with additive noise when SI was used. Section IV gives examples of iterative restoration for blur reduction in SPOT 1, high-resolution visible, HRV-2,10-m panchromatic band images at both the original and the two-times enlarged image size caused by smoothing-interpolation. Section V gives conclusions on these results. Note that when the iterations are limited, the result is a partially restored image. Subjectively, it may be an acceptable compromise between blur reduction and noise amplification. SECTION I. INVERSE FILTER RESTORATION The following discussion assumes a simple model of the imaging sensor system in which the degraded image g(i, /), sensor system PSF h(i, /), and original image fli, f) are assumed to be discrete. As defined in this study, the objective of restoration is to determine a discrete estimate of the original continuous image. The image is then observed as a continuous image on a computer device, typically at a magnified several times scale. Additional degradations from the display system were not considered in this study. The noise amplification problem common to inverse filtering is outlined next (Andrews, 1974). Original image W.j) Blur PSF Degraded image Figure 1. System model. The system model of figure 1 can be expressed as (1) where g(i, j) is the degraded image, h(i, f) is the PSF, the optical impulse response; * denotes convolution; and /(/, f) is the original, undegraded, and assumed discrete image. The frequency domain equivalent of equation 1 is (2) where F, G, and H denote the Fourier transform of/, g, and h, respectively; CO;, 0)2 are spatial frequency variables; and //(CQ/, 0)2) is the system transfer function. Inverse filter restoration of equation 2 to obtain F(W;, 0)2) is 02) 0) where ! ///(«/, 0)2) is the inverse filter for restoration. Including additive noise, n(i, /), in the system model of figure 1 (equation 1) gives figure 2. Original image Blur PSF, Blur degraded image plus noise Figure 2. System model with additive noise degradation. The model of figure 2 can be expressed as g(i,j) = h(i,j) */(/,./) + n(i,j) (4)