## 1 Introduction  
The imaging correlography technique was first proposed by [PERSON] and [PERSON] [1; 2; 3]. It can construct a high-resolution image of a laser-illuminated object from the measurements of backscattered laser speckle intensity patterns. Imaging correlography is based on the fact that the autocorrelation function of the object's brightness distribution can be estimated from the average energy spectrum of the measured speckle intensity images. Previous work has demonstrated that the Fourier transform of the autocorrelation of the object's brightness function is equal to the squared modulus of the Fourier transform of the object [4]. If the phase information associated with this Fourier transform can be retrieved, one can reconstruct the object by inverse Fourier transform of the synthesized Fourier data. The imaging correlography technique can recover the object using only the knowledge of the Fourier modulus, without needing phase information. It is insensitive to atmospheric turbulence and the optical imperfection of the device [5; 6]. To obtain a Fourier magnitude estimate that is acceptable for reconstructing the object, in practical applications a large amount of speckle-intensity images is required. Moreover, the estimated Fourier modulus is noisy and loses a lot of high-frequency information, which makes it difficult for the phase retrieval algorithm to converge on the optimal global value [7; 8]. In recent years, [PERSON] et al. used imaging correlography for high-resolution retinal imaging to overcome ocular aberrations [9]. Based on the shower curtain effect, [PERSON] et al. proposed a novel speckle correlography protocol that is insensitive to turbid medium motions. Additionally, they extended the correlography technique to transmitting or other nonscattering objects by illuminating the object with a speckle pattern [10]. Ptychography is a popular phase imaging technique for reconstructing a high-resolution image of a specimen from a series of diffraction patterns. It could only be applied to crystalline objects when it was first proposed by [PERSON] in the 1970s [11]. After the Wigner distribution deconvolution method (WDMM) was proposed by [PERSON] and [PERSON], it could also be used to recover amorphous objects [12]. A breakthrough in ptychography was achieved in 2004; that is, an iterative algorithm named the ptychographic iterative engine (PIE) was applied to solve this phase problem [13]. In ptychography, a light probe is fixed on a translation stage, which can shift laterally with respect to the optical axis, such that probes at neighboring positions overlap with each other. The far-field diffraction patterns are recorded at each probe position, and then the object can be reconstructed with an iterative image reconstruction algorithm. This has been realized with electron beams [14], hard X-rays [15], and visible light [16]. Compared with other phase imaging techniques, such as interferometers [17] and digital holography [18], ptychography can obtain high-resolution and large field-of-view (FOV) images without complex optical systems or precise imaging applications. In the previous microscopic applications, the imaging targets for ptychography were thin biological samples that naturally have a smooth phase. However, the imaging samples for long-distance imaging systems are daily objects with \"optically rough\" surfaces. The variable height function of the surface introduces the rapidly changed random phase for the object. Because of the self-interference of coherent light backscattered from the object's rough surface, the transmitted field forms as speckle patterns in the detection plane [19; 20; 21; 22]. [PERSON] et al. realized the reconstruction of optically rough objects with Fourier ptychography [20; 21]. Compared with conventional ptychography techniques, such as PIE, low-resolution images are measured in the image plane rather than the far-field diffraction patterns. A previous research studied utilized ptychography with a pseudothermal source [23].