Quantification of wheezing by a sensor system consisting of a wearable wireless acoustic sensor and smartphone performing respiratory sound classification may contribute to the diagnosis, long-term control, and lowering treatment costs of asthma. In such battery-powered sensor system, compressive sensing (CS) was verified as a method for simultaneously cutting down power cost of signal acquisition, compression, and communication on the wearable sensor. Matching real-time CS reconstruction algorithms, such as orthogonal matching pursuit (OMP), have been demonstrated on the smartphone. However, their lossy performance limits the accuracy of wheeze detection from CS-recovered short-term Fourier spectra (STFT), when using existing respiratory sound classification algorithms. Thus, here we present a novel, robust algorithm tailored specifically for wheeze detection from the CS-recovered STFT. The proposed algorithm identifies occurrence and tracks multiple individual wheeze frequency lines using hidden Markov model. The algorithm yields 89.34% of sensitivity, 96.28% of specificity, and 94.91% of accuracy on Nyquist-rate sampled respiratory sounds STFT. It enables for less than 2% loss of classification accuracy when operating over STFT reconstructed by OMP, at the signal compression ratio of up to 4 $\times$ (classification from only 25% signal samples). It features execution speed comparable to referent algorithms, and offers good prospects for parallelism.