It has recently been demonstrated that object recognition can be formulated as an image-restoration problem. In this approach, which we term impulse restoration, the objective is to restore a delta function that indicates the detected object's location. We develop solutions based on impulse restoration for the Gaussian-noise case. We propose a new iterative approach, based on the expectation-maximization (EM) algorithm, that simultaneously estimates the background statistics and restores a delta function at the location of the template. We use a Monte Carlo study and localization-receiver-operating-characteristics curves to evaluate the performance of this approach quantitatively and compare it with existing methods. We present experimental results that demonstrate that impulse restoration is a powerful approach for detecting known objects in images severely degraded by noise. Our numerical experiments point out that the proposed EM-based approach is superior to all tested variants of the matched filter. This result demonstrates that accurate modeling and estimation of the background and noise statistics are crucial for realizing the full potential of impulse restoration-based template matching.

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We investigate the problem of detecting and localizing a known signal in a photon-limited image, where Poisson noise is the dominant source of image degradation. For this purpose we developed and evaluated three new algorithms. The first two are based on the impulse restoration (IR) principle and the third is based on the generalized likelihood ratio test (GLRT). In the IR approach, the problem is formulated as one of restoring a delta function at the location of the desired object. In the GLRT approach, which is a well-known variation on the optimal likelihood ratio test, the problem is formulated as a hypothesis testing problem, in which the unknown background intensity of the image and the intensity scale of the object are obtained by maximum-likelihood estimation. We used Monte Carlo simulations and localization receiver operating characteristic (LROC) curves to evaluate the proposed algorithms quantitatively. LROC curves demonstrate the ability of an algorithm to detect and locate objects in a scene correctly. Our simulations demonstrate that the GLRT approach is superior to all other tested algorithms.

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