Object counting, defined as the task of accurately predicting the number of objects in static images or videos, has recently attracted considerable interest. However, the unavoidable presence of background noise prevents counting performance from advancing further. To address this issue, we created a group and graph attention network (GGANet) for dense object counting. GGANet is an encoder-decoder architecture incorporating a group channel attention (GCA) module and a learnable graph attention (LGA) module. The GCA module groups the feature map into several subfeatures, each of which is assigned an attention factor through the identical channel attention. The LGA module views the feature map as a graph structure in which the different channels represent diverse feature vertices, and the responses between channels represent edges. The GCA and LGA modules jointly avoid the interference of irrelevant pixels and suppress the background noise. Experiments are conducted on four crowd-counting datasets, two vehicle-counting datasets, one remote-sensing counting dataset, and one few-shot object-counting dataset. Comparative results prove that the proposed GGANet achieves superior counting performance.

The optimisation of measurement matrix that is within the compressive sensing framework is considered in this study. Based on the fact that an information factor with smaller mutual coherence performs better, the gradient measurement matrix optimisation method is improved by an orthogonal search direction revision factor. This algorithm updates the approximation of ideal Gram matrix of information operator and the measurement matrix alternatingly. Using measurement matrix and sparse basis to represent the Gram matrix, the measurement matrix is optimised by the gradient algorithm, in which an orthogonal gradient search direction revision factor is proposed and utilised to further improve the performance of measurement matrix. This orthogonal factor is computed by the Cayley transform of a real skew symmetric matrix that is related to the gradient and the measurement matrix. Results of several experiments show that compared with the initial random matrix, the optimised measurement matrix can lead to better signal reconstruction quality.