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Laser speckle contrast imaging is widely used in clinical studies to monitor blood flow distribution. Speckle contrast tomography, similar to diffuse optical tomography, extends speckle contrast imaging to provide deep tissue blood flow information. However, the current speckle contrast tomography techniques suffer from poor spatial resolution and involve both computation and memory intensive reconstruction algorithms. In this work, we present SpeckleCam, a camera-based system to reconstruct high resolution 3D blood flow distribution deep inside the skin. Our approach replaces the traditional forward model using diffuse approximations with Monte-Carlo simulations-based convolutional forward model, which enables us to develop an improved deep tissue blood flow reconstruction algorithm. We show that our proposed approach can recover complex structures up to 6 mm deep inside a tissue-like scattering medium in the reflection geometry. We also conduct human experiments to demonstrate that our approach can detect reduced flow in major blood vessels during vascular occlusion.