In Single Photon Emission Computed Tomography (SPECT), the image reconstruction process involves many tunable parameters that have a significant impact on the quality of the resulting clinical images. Traditional image quality evaluation often relies on expert judgment and full-reference metrics such as MSE and SSIM. However, these approaches are limited by their subjectivity or the need for a ground-truth image. In this paper, we investigate the usage of a no-reference image quality assessment method tailored for SPECT imaging, employing the Perception-based Image QUality Evaluator (PIQUE) score. Precisely, we propose a novel application of PIQUE in evaluating SPECT images reconstructed via filtered backprojection using a parameter-dependent Butterworth filter. For the optimization of filter's parameters, we adopt a kernel-based Bayesian optimization framework grounded in reproducing kernel Hilbert space theory, highlighting the connections to recent greedy approximation techniques. Experimental results in a concrete clinical setting for SPECT imaging show the potential of this optimization approach for an objective and quantitative assessment of image quality, without requiring a reference image.