In a pure estimation task, a signal is known to be present, and we wish to determine numerical values for parameters that describe it. We compared the performance of the classical Wiener estimator and a new scanning-linear estimator for the task of estimating signal location, signal volume, and signal amplitude from noisy image data. Both procedures incorporate prior knowledge of the data's statistical fluctuations and minimize a given metric of error. First we explore the classical Wiener estimator, which operates linearly on the data and minimizes .the ensemble mean-squared error among linear methods. The signal is embedded in random background to simulate the effect of nuisance parameters. The results of our performance tests indicate the Wiener estimator is fundamentally unable to locate a signal, regardless of the quality of the image, when the background is random. Even when the simulated relationship between the object and image was reduced to noisy samples of planar objects, linear operations on.the data failed to locate the signal. Given these new results on the fundamental limitations of Wiener estimation, we extend our methods to include more complex data processing. We introduce and evaluate a scanninglinear estimator that performs impressively. The scanning action of the estimator refers to seeking a solution that maximizes a linear metric, thereby requiring a global-extremum search. The linear metric to be optimized can be derived as a special case of maximum a posteriori (MAP) estimation when the likelihood is Gaussian and a slowly-varying covariance approximation is made.