## 1 Introduction
However, their imaging method requires the detector to measure the speckle patterns within the coherence time of the intensity fluctuations. The intensity fluctuations for the thermal source are in the order of tens of femtoseconds, meaning most detectors are not fast enough to record it. [PERSON] and [PERSON] et al. [24; 25] imaged extended objects using the ptychographic speckle correlation method, which is based on the \"memory effect\" of speckles [26; 27; 28]. This method can realize noninvasive imaging with a single speckle pattern. However, the illuminated area for each position is chosen to satisfy both the memory effect range and practical limits of the detector. Therefore, it is more suitable for biomedical and materials research. In this work, we join imaging correlography and ptychography together. A practical implementation of imaging correlography using ptychography is illustrated schematically in Figure 1. The laser beam passes over a long distance to form an illumination spot of a certain size. Scanning measurements can be realized by changing the illumination angle of the laser source. Different deflection angles correspond to different overlapping areas. Here, red circles indicate scanning positions for ptychographic measurements. The solid black line represents the imaging process for the first position,and the dotted blue line represents the imaging process for the second position with the change of illumination angle. Instead of illuminating the whole object, we measure the object part-by-part in a ptychographic way. Then, imaging correlography is used to estimate the Fourier modulus of each part of the object based on the measured far-field speckle patterns. Finally, the phase retrieval algorithm is applied to reconstruct the object. For Figure 1, the speckle patterns are formed by atmospheric turbulence. In some cases, the atmospheric turbulence effect is not strong enough to provide sufficient signal flux at the camera face. The independent patterns of the observed speckle intensity can be measured by translating the detector or rotating the object [2; 3; 7; 8; 29]. These measurements can also be achieved by directly illuminating the object with the speckle pattern, which is proposed in previous work [10]. Reconstructing images from astronomical speckle data is analogous to recovering images from speckle patterns as one rotates the object [8]. In both cases, the recorded speckle data can be processed to obtain an estimate of the Fourier magnitude of the object. Then, by using a phase retrieval algorithm, the object can be reconstructed. In the proposed imaging method, we make three contributions. Firstly, the correlography and ptychography are joined together to solve the problem of inaccurate phase recovery in the imaging correlography. Secondly, the Fourier magnitude is estimated for ptychographic reconstruction using imaging correlography. Finally, the new initialization method and optimization framework are employed to the ptychographic imaging correlography. Moreover, a novel image space denoising regularization is plugged into the loss function to reduce the effects of reconstruction noise and improve the perceptual quality of the recovered image.