## 1 Introduction
Multiwavelength digital holography has an enhanced ability for 3D wide-range shape measurements by using multiwavelength phase unwrapping, due to the recording of multiwavelength quantitative phase information. The multiwavelength is an effective instrument enabling good phase and data diversity in phase retrieval. The multiwavelength absolute phase imaging is much less studied as compared with the standard single-wavelength formulation. These works by the principle of measurements can be separated in two groups. In interferometry and holography scenarios the reference beams are applied to reveal the phase information, e.g., [35; 36; 37; 38; 39; 40]. After that, the phase unwrapping algorithms for 2D images are applied. Recently, the phase unwrapping with simultaneous processing of multiwavelength complex-exponent observations have been developed based on the maximum likelihood techniques [41; 42]. Another group of the multiwavelength absolute phase imaging techniques uses as measurements amplitudes or intensities of coherent diffraction patterns of an object without reference waves. In these intensity measurements the phase information is missing. These formulations are from the class of the multiwavelength phase retrieval problems, e.g., [43; 44; 45; 46; 47; 48]. The Chinese Remainder Theorems, existing in many modifications, provide methods for absolute phase reconstruction from multiwavelength data for noiseless data [49]. The reformulation of these mathematically strong approaches for more practical scenarios with noisy data and for robust estimation leads to the techniques similar to various forms of maximum likelihood [50; 51]. In this paper we study the problem of multiwavelength absolute phase retrieval from noisy object diffraction patterns with no reference beams. The system is lensless with multiwavelength coherent input light beams and random phase masks applied for wavefront modulation. The light beams are formed by light sources radiating all wavelengths simultaneously and a Complementary MetalOxide Semiconductor (CMOS) sensor equipped by a Color Filter Array (CFA) is used for spectral measurement registration. The developed algorithm is based on maximum likelihood optimization, in this way targeted on optimal phase retrieval from noisy observations. The algorithm valid for both Poissonian and Gaussian noise distributions is presented. One of the key elements of the algorithm is an original sparse modeling of the multiwavelength complex-valued images based on the complex-domain block-matching 3D filtering. Numerical experiments demonstrate that the developed algorithm lead to the effective solutions explicitly using the sparsity for noise suppression and enabling accurate reconstruction of absolute phase for high-dynamic range of variations. In this work, we use the approach which can be treated as a development of the Sparse Phase and Amplitude Reconstruction (SPAR) algorithms [32; 33] and the maximum likelihood absolute phase reconstruction for multiwavelength observations [42]. This approach has been exploited in our paper [52] for absolute phase retrieval from multifrequency in the different setup with observations obtained for multiple single wavelength experiments. Remind, that in this paper the experiments are multiwavelength and phase information for each wavelength is retrieved by the developed wavelength multiplexing algorithm.