In practical target detection, we often deal with situations where even a relatively small target is present in two or more adjacent pixels, due to its physical configuration with respect to the pixel grid. At the same time, a relatively large but narrow object (such as a wall or a narrow road) may be collectively present in many pixels but be only a small part of each single pixel. In such cases, critical information about the target is spread among many spectra and cannot be used efficiently by detectors that investigate each single pixel separately. We show that these difficulties can be overcome by using appropriate smoothing operators. We introduce a class of Locally Adaptive Smoothing detectors and evaluate them on three different images representing a broad range of blur that would interfere with the detection process in practical problems. The smoothing-based detectors prove to be very powerful in these cases, and they outperform the traditional detectors such as the constrained energy minimization (CEM) filter or the one-dimensional target-constrained interference-minimized filter (TCIMF).