The use of the FDR method of multiple hypothesis testing when inverting linear homogeneous operators

One of the important tasks when processing large data arrays is their economical representation. To solve this task, it is necessary to identify significant features and remove noise. Such problems are found in a wide variety of fields such as genetics, biology, astronomy, computer graphics, audio and video data processing, etc. Modern research in this area describes various filtering methods based on a sparse representation of the obtained experimental data. To construct statistical estimates based on the observed data, the procedure of multiple testing of hypotheses about the significance of observations is widely used. The present authors consider the FDR (false discovery rate) method based on the control of the expected proportion of false rejections of the null hypothesis and the Benjamin–Hochberg algorithm for multiple hypothesis testing. Often, the information available for observation is some kind of transformation of the data of interest. This additionally raises the problem of inverting this transformation. The present authors consider the case when the original data vector is subjected to some linear homogeneous transformation. Such situations are typical, for example, in astrophysical and tomographic applications.