Schematic overview of SpaSRL enhancing-decoding (A&B) processes and potential applications of SpaSRL in downstream SRT analysis (C). (A) Spatial expression enhancement from aggregating expression information from neighbourhood spots. SpaSRL incorporates spatial information into gene expression to enhance the shared expression between spots by flexibly aggregating the weighed gene expression from their |$k$| spatial neighbors (e.g. |${X}^0\to X$|⁠). |$S$| denotes the weight of expression similarity between each spot and its |$k$| neighbors. |$\alpha$| controls the contribution of spatial similarity to the enhanced expression measurements. (B) Spatial expression decoding via the feature extraction embedded self-representation learning model. The input data (i.e. |$X$|⁠) is the enhanced gene expression matrix from (A). SpaSRL uses a robust projection matrix (i.e. |$P$|⁠) to generate the low-dimensional representation (i.e. |$X\to PX,{P}^T PX=X$|⁠). Based on the original and low-dimensional data, SpaSRL performs data reconstructions via an aggregated weight matrix |$Z$| based on self-representation learning algorithm (i.e. |$X= XZ$| and |$PX= PXZ$|⁠). SpaSRL iteratively learns the projection matrix (i.e. |$P$|⁠) and spot–spot similarity matrix (i.e. |$Z$|⁠) by minimizing the sum of reconstruction losses (see Methods). When SpaSRL reaches convergence, the two optimal matrices are achieved for further downstream analyses. (C) Biological applications for SpaSRL including spatial domain identification, functional genes/meta genes identification and data denoising. The spot–spot similarity matrix can be applied to detect spatial domains and data denoising. The projection matrix can be employed to identify functional genes/meta genes to improve biological insights into tissue heterogeneity.