## 1 Introduction  
Reconstruction of a wavefront phase is on demand in holography [1; 2], interferometry [3], holographic tomography [4; 5] and is of general interest due to important practical applications in such areas as biomedicine (for instance for studies of living cells [6; 7]), 3D-imaging [8], micromachining [9], etc. There are two different approaches for extraction of spatial phase information. The first, which is associated with the holography, implies recording interference patterns of object and reference waves, while the second approach involves only sets of coherent diffraction patterns of object without reference waves. In these intensity measurements the phase information of the registered wavefields is eliminated, and then reconstructed by means of numerical iterative algorithms. The latter problem is well known as the phase retrieval, where \"phase\" emphasizes that the missing phase defines the principal difficulty of the problem and its difference with respect to holography. The first phase retrieval algorithm was introduced by [PERSON] and [PERSON] [10]. They used squared roots of intensities measured in image plane to replace amplitudes calculated in iterations. Important update was developed by [PERSON] [11], who introduced constrains for the iterative process by the amplitude distribution in Fourier plane, namely, a nonnegativity of the reconstructed image and energy concentration in a certain area. A dataset of recorded intensity patterns which is characterizedby diversity of one or several parameters of the optical setup is a crucial moment of the phase retrieval problems. Defocusing and phase modulation are known as effective instruments in order to achieve the measurement diversity sufficient for reliable phase reconstruction (e.g., [12; 13; 14; 15]). Various types of diffraction optical elements can be used for design of phase imaging systems [16]. The review and analysis of this type of the systems as well as further developments of the algorithms can be found in [17]. There are various optimization formulations of conventional Gerchberg-Saxton (GS) algorithm [18; 19; 20]. Contrary to the intuitively clear heuristic of the GS algorithm, the variational approaches have a stronger mathematical background including image formation modeling, formulation of the objective function (criterion) and finally going to numerical techniques solving corresponding optimization problems. The recent overview [21] is concentrated on the algorithms for the phase retrieval with the Fourier transform measurements and applications in optics. The constrains sufficient for uniqueness of the solution are presented in detail. The fundamental progress for the methods based on the convex matrix optimization is announced in [22], where the novel algorithm \"Sketchy Decisions\" is presented. This algorithm is effective for high dimensions typical for the phase-lifting methods and is supported by the mathematical analysis and the convergence proof. The Wirtinger flow (WF) and truncated Wirtinger flow (TWF) algorithms presented in [23; 24] are iterative complex-domain gradient descent methods applied to Gaussian and Poissonian likelihood criteria, respectively. The techniques based on the proximity operators developed in [25; 26] provide a regularized optimization of the maximum likelihood criteria also for both Gaussian and Poissonian observations. The sparsity based techniques is a hot topic in phase retrieval (e.g., [27]). A sparse dictionary learning for phase retrieval is demonstrated in [28]. The transform domain phase and amplitude sparsity for phase imaging is developed in [29; 30; 31]. For the phase retrieval these techniques are applied in [32; 33; 34]. In recent years, there has been an increase in demand for multispectral imaging. Multispectral information by recording object waves with multiple wavelengths that are irradiated from multiwavelength light sources helps to analyze and recognize objects, to clarify color and tissue distributions and dramatically improves the quality of imaging.