Photoacoustic tomography (PAT) is a propitious imaging modality, which is helpful for biomedical study. However, fast PAT imaging and denoising is an exigent task in medical research. In order to accomplish the fast PAT imaging task, this study investigates the subsampling artifacts problem in Photoacoustic Tomography (PAT) recovery as a by-product due to not following the Nyquist Sampling Theorem. Generally, to reduce the computational cost, PAT images recover by taking low measurements from the sensors into account which consequently produce artifacts and deteriorate the image quality. In this paper, a novel inverse compressed sensing (iCS) based approach is instigated as a first part which takes few measurements from the sensors and recover PAT images. The purpose of using the iCS approach is to mainly diminish the sparsity requirements (to make image sparse according to the nature of image) which is mainly beneficial for real world data as well. As a second part, a deep learning-based solution is employed as a post processor which particularly remove these under-sampled artifacts and provides high quality photoacoustic images at the output. Moreover, the results are validated qualitatively and quantitively by statistical measures i.e., structural similarity index metric (SSIM) and peak signal to noise ratio (PSNR). It can be seen through statistical analysis that the quality is significantly improved by 30% (approximately), having average SSIM = 0.974 and PSNR = 29.88 dB with standard deviation ±0.007 and ±0.089, respectively.