The sparse transforms currently used in the model-based reconstruction method for photoacoustic computed tomography (PACT) are predefined and they typically cannot capture the underlying features of the specific data sets adequately, thus limiting the high-quality recovery of photoacoustic images. In this work, we present an advanced reconstruction model using the K-VSD dictionary learning technique and present the in vivo results after adapting the model into the 3D PACT system. The in vivo experiments were performed on an IRB approved human hand and two rats. When compared to the traditional sparse transform, experimental results using our proposed method improved accuracy and contrast to noise ration of the reconstructed photoacoustic images, on average, by 3.7 and 1.8 times in the case of 50% sparse-sampling rate, respectively. We also compared the performance of our algorithm against other techniques, and imaging speed was 60% faster than other approaches. Our system would require sparse-transducer array and lower number of data acquisition hardware (DAQs) potentially reducing the cost of the system. Thus, our work provides a new way for reconstructing photoacoustic images, and it would enable the development of new high-speed low-cost 3D PACT for various biomedical applications.