Ovarian cancer detection has traditionally relied on a multi-step process that includes biopsy, tissue staining, and morphological analysis by experienced pathologists. While widely practiced, this conventional approach suffers from several drawbacks: it is qualitative, time-intensive, and heavily dependent on the quality of staining. Mid-infrared (MIR) hyperspectral photothermal imaging is a label-free, biochemically quantitative technology that, when combined with machine learning algorithms, can eliminate the need for staining and provide quantitative results comparable to traditional histology. However, this technology is slow. This work presents a novel approach to MIR photothermal imaging that enhances its speed by an order of magnitude. Our method significantly accelerates data collection by capturing a combination of highresolution and interleaved, lower-resolution infrared band images and applying computational techniques for data interpolation. We effectively minimize data collection requirements by leveraging sparse data acquisition and employing curvelet-based reconstruction algorithms. This approach enhances imaging speed without compromising image quality and ensures robust tissue segmentation. This method resolves the longstanding trade-off between imaging resolution and data collection speed, enabling the reconstruction of high-quality, high-resolution images from undersampled datasets and achieving a 10X improvement in data acquisition time. We assessed the performance of our sparse imaging methodology using a variety of quantitative metrics, including mean squared error (MSE), structural similarity index (SSIM), and tissue subtype classification accuracies, employing both random forest and convolutional neural network (CNN) models, accompanied by Receiver Operating Characteristic (ROC) curves. Our statistically robust analysis, based on data from 100 ovarian cancer patient samples and over 65 million data points, demonstrates the method's capability to produce superior image quality and accurately distinguish between different gynecological tissue types with segmentation accuracy exceeding 95%. Our work demonstrates the feasibility of integrating rapid MIR hyperspectral photothermal imaging with machine learning in enhancing ovarian cancer tissue characterization, paving the way for quantitative, label-free, automated histopathology. It represents a significant leap forward from traditional histopathological methods, offering profound implications for cancer diagnostics and treatment decision-making.