Textures or high-detailed structures contain information that can be exploited in pattern recognition and classification. If an acquired image is noisy, noise removal becomes an operation to improve image quality before further stages of processing. Among possible variants of denoising, we consider filters based on orthogonal transforms, in particular, on discrete cosine transform (DCT) known to be able to effectively remove additive white Gaussian noise (AWGN). Besides, we study a representative of nonlocal denoising techniques, namely, BM3D known as state-of-the-art technique based on DCT and similar patch search. We show that noise removal in texture images using the considered DCT-based techniques can distort fine texture details. To detect such situations and avoid texture degradation due to filtering, we propose to apply filtering efficiency prediction tests applicable to wide class of images. These tests are based on DCT coefficient statistic parameters and can be used for decision-making in relation to the use of the considered filters.