In this paper we propose automatic image denoising method based on Hermite functions (HeNLM). It is an extension of non-local means (NLM) algorithm. Differences between small image blocks (patches) are replaced by differences between feature vectors thus reducing computational complexity. The features are calculated in coordinate system connected with image gradient and are invariant to patch rotation. HeNLM method depends on the parameter that controls filtering strength. To chose automatically this parameter we use a no-reference denoising quality assessment method. It is based on Hessian matrix analysis. We compare the proposed method with full-reference methods using PSNR metrics, SSIM metrics, and its modifications MSSIM and CMSC. Image databases TID, DRIVE, BSD, and a set of dermatological immunofluorescence microscopy images were used for the tests. It was found that more perceptual CMSC and MSSIM metrics give worse correspondence than SSIM and PSNR to the results of information preservation by the non-reference image denoising.