Blood cell detection and counting in holographic lens-free imaging by convolutional sparse dictionary learning and coding

We propose a convolutional sparse dictionary learning and coding approach for detecting and counting instances of a repeated object in a holographic lens-free image. The proposed approach exploits the fact that an image containing a single object instance can be approximated as the convolution of a (small) object template with a spike at the location of the object instance. Therefore, an image containing multiple non-overlapping instances of an object can be approximated as the sum of convolutions of templates with spikes. Given one or more images, one can learn a dictionary of templates using a convolutional extension of the K-SVD algorithm for sparse dictionary learning. Given a set of templates, one can efficiently detect object instances in a new image using a convolutional extension of the matching pursuit algorithm for sparse coding. Experiments on red blood cell (RBC) and white blood cell (WBC) detection and counting demonstrate that the proposed method produces promising results without requiring additional post-processing.