The flow field in a compressor is circumferentially non-uniform due to the wakes from upstream stators, the potential field from both upstream and downstream stators, and blade row interactions. This non-uniform flow impacts stage performance as well as blade forced vibrations. Historically, experimental characterization of the circumferential flow variation is achieved by circumferentially traversing either a probe or the stator rows. This involves the design of complex traverse mechanisms and can be costly. To address this challenge, a novel method is proposed to reconstruct compressor nonuniform circumferential flow field using spatially under-sampled data points from a few probes at fixed circumferential locations. The paper is organized into two parts. In the present part of the paper, details of the multi-wavelet approximation for the reconstruction of circumferential flow and use of the Particle Swarm Optimization algorithm for selection of probe positions are presented. Validation of the method is performed using the total pressure field in a multi-stage compressor representative of small core compressors in aero engines. The circumferential total pressure field is reconstructed from 8 spatially distributed data points using a triple-wavelet approximation method. Results show good agreement between the reconstructed and the true total pressure fields. Also, a sensitivity analysis of the method is conducted to investigate the influence of probe spacing on the errors in the reconstructed signal.