the focus of this paper is to consider the compressed sensing problem. it is stated that the compressed sensing theory, under certain conditions, helps relax the nyquist sampling theory and takes smaller samples. one of the important tasks in this theory is to carefully design measurement matrix (sampling operator). most existing methods in the literature attempt to optimize a randomly initiali...

Testing a sequence of pre-ordered hypotheses to decide which of these can be rejected or accepted while controlling the familywise error rate (FWER) is of importance in many scientific studies such as clinical trials. In this paper, we first introduce a generalized fixed sequence procedure whose critical values are defined by using a function of the numbers of rejections and acceptances, and wh...

2 Methods 5 2.1 Multiple hypothesis testing framework . . . . . . . . . . . . . 5 2.2 Test statistics null distribution . . . . . . . . . . . . . . . . . 11 2.3 Single-step procedures for control of general Type I error rates θ(FVn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Step-down procedures for control of the family-wise error rate 16 2.5 Augmentation multiple tes...

We consider a clinical trial with a primary and a secondary endpoint where the secondary endpoint is tested only if the primary endpoint is significant. The trial uses a group sequential procedure with two stages. The familywise error rate (FWER) of falsely concluding significance on either endpoint is to be controlled at a nominal level α. The type I error rate for the primary endpoint is cont...

A new general algorithm for computing distance transforms of digital images is presented. The algorithm consists of two phases. Both phases consist of two scans, a forward and a backward scan. The first phase scans the image column-wise, while the second phase scans the image row-wise. Since the computation per row (column) is independent of the computation of other rows (columns), the algorith...

The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initiali...