The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problems

Tumor spheroid elasticity estimation using mechano-microscopy combined with a conditional generative adversarial network

“…2.3) from the elasticity images produced by the generator, while the generator is trained to fool the critic by producing elasticity images that resemble the ground truth elasticity images. The loss function, ℒ(𝑑, 𝑔), is described in detail by Ray et al [47] and shown in Eq. 3, where 𝑑(𝑥, 𝑦) is the output from the critic; 𝑔(𝑧, 𝑦) is the output from the generator; (𝑥, 𝑦) represents an elasticity/phase difference image pair from the true distribution, 𝑝 𝑥𝑦 ; 𝑧 represents the latent vector from the latent space, 𝑝 𝑧 ; 𝒢𝒫 is the gradient penalty term used to enforce Lipschitz continuity on the critic, and 𝔼 denotes the expectation value.…”

“…As shown in Figure 1a, the generator consists of a contracting path (in which the image is progressively downsampled to enable feature extraction at different scales) followed by an expanding path (in which the image is progressively upscaled to achieve the desired output dimensions), with skip connections that transfer learned features from the contracting path to the expanding path. Conditional instance normalization is used to inject the latent vector at each scale of the generator, as outlined by Ray et al [47].…”

“…2.3) from the elasticity images produced by the generator, while the generator is trained to fool the critic by producing elasticity images that resemble the ground truth elasticity images. The loss function, ℒ(𝑑, 𝑔), is described in detail by Ray et al [47] and shown in Eq. 3,…”

“…The cGAN architecture was based on a structure previously described by Ray et al [47]. Briefly, the cGAN consists of two parts, a generator, and a critic.…”

“…For example, in ultrasound elastography, cGANs have been used to synthesize elasticity given prior knowledge of the sample structure and/or displacement [46][47][48]. The problem of spheroid elasticity estimation with micro-scale resolution is particularly suited to cGANs since, at this scale, spheroids can be represented parametrically (e.g., in terms of the number of cells, cell size, and nucleus elasticity), thus enabling the training set to be generated by simulation using FEA.…”