## 1 Introduction  
Digital optical holography of particles [1, 2, 3] is one of the methods for the noninvasive study of particles of different origins in different media. The principle of holographic recording makes it possible to register information on all particles of the studied medium volume per exposure and further analyze their reconstructed holographic images. An in-line holographic scheme is typically used to study particles when the radiation scattered on the particles represents a subject wave and the radiation that passed without scattering is a reference wave. A hologram is an interference pattern of these waves recorded on any carrier (photoemulsion, charge-coupled device (CCD), or complementary metal-oxide semiconductor (CMOS) matrix). The interference pattern for registration must be stable during exposure, which is ensured by a short pulse of coherent radiation. At the same time, this may cause undesirable effects associated with the coherence of radiation--coherent noises in the reconstructed image related to the parameters of the medium with the analyzed particles, as well as to the twin-image effect of the studied particle [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. The latter appears due to the fact that the reconstruction of a real particle image from a hologram by illuminating it with a coherent wave (or numerical modeling of lighting in digital holography) leads to the simultaneous reconstruction of the virtual image of this particle. The interference of waves corresponding to these images deteriorates the quality of the reconstructed image and reduces the accuracy of its focusing and classification. There are special difficulties in studying particle images when this effect is observed for several closely spaced particles. Two known methods of suppressing the twin-image effect are considered as examples in the article: a complex field amplitude reconstruction method based on the Gerchberg-Saxton algorithm and a spatial-frequency method having a different physical and algorithmic basis. The main task of the study of these methods is to determine whether the boundary conditions for their use depend on their physical basis or, to a greater extent, are determined by the features of the quality indicators of the particle holographic image. This implies the use of the previously proposed quantitative indicators of the quality of particle images (boundary contrast and boundary intensity jump), which are compared and applied in the article along with other existing methods (mean square error (MSE), signal-to-noise ratio (SNR) or peak signal-to-noise ratio (PSNR), dispersion of image intensity, distinctive ability). Another source of coherent noise is the cross-interference of waves scattered on particles and the turbulence of the medium. This noise also reduces the quality of particle images and makes it difficult to recognize them. Here, to reduce this noise, a well-known method--averaging--is also considered. The paper also studies whether the number of averages required to achieve the quality of images of particles reconstructed from a hologram sufficient for their recognition by the distinguishability parameter depends on the averaging method. The averaging method means the averaging of holograms, the averaging of reconstructed holographic images, the multispectral recording of a hologram, or multispectral image reconstruction. This paper considers some practical issues related to the use of well-known methods for suppressing the above-mentioned coherent noises, their efficiency, and their limits of applicability. There may be no conditions or possibilities for complete suppression in a real holographic experiment.