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N-finder algorithm (N-FINDR) has been widely used for endmember extraction in hyperspectral imagery. Due to its high computational complexity, developing fast computing N-FINDR has received considerable interest, specifically to take advantage of field-programmable gate array (FPGA) architecture in hardware implementation to realize N-FINDR. However, there are two severe drawbacks arising in the nature of N-FINDR design, the number of endmembers, p, which must be fixed once its value is determined in FPGA design and inconsistency in final extracted endmembers caused by different selections of initial endmembers. This paper investigates a progressive version of N-FINDR, previously known as simplex growing algorithm for its FPGA implementation which can resolve these two issues.

Fully constrained least squares (FCLS) method has been widely used in linear spectral mixture analysis (LSMA). This paper presents a progressive endmember growing method by FCLS, to be called Endmember Growing FCLS (EG-FCLS). Its idea is derived from a commonly used endmember finding algorithm, Simplex Growing Algorithm (SGA) where the criterion of finding maximal simplex volume is replaced by least squares error unmixed by FCLS.

This paper presents a progressive band processing (PBP) version of an endmember finding algorithm, simplex growing algorithm (SGA), to be called PBP-SGA, which allows users to perform SGA band by band progressively. Several advantages can be gained from this approach. First of all, PBP-SGA does not require data dimensionality reduction since PBP begins with a lower band dimension and gradually increases band dimensions band by band progressively until it achieves the desired results. Secondly, PBP can process SGA whenever bands are available without waiting for the information from all band information to be received. As a result, PBP-SGA can be used for data transmission and communication. Thirdly, PBP-SGA can help identify which bands are crucial during the process of finding endmembers. Finally, PBP-SGA provides feasibility of being implemented in real time according to Band SeQuential (BSQ) format.

International audience; In hyperspectral imaging, spectral unmixing is one of the most challenging and fundamental problems. It consists of breaking down the spectrum of a mixed pixel into a set of pure spectra, called endmembers, and their contributions, called abundances. Many endmember extraction techniques have been proposed in literature, based on either a statistical or a geometrical formulation. However, most, if not all, of these techniques for estimating abundances use a least-squares solution. In this paper, we show that abundances can be estimated using a geometric formulation. To this end, we express abundances with the barycentric coordinates in the simplex defined by endmembers. We propose to write them in terms of a ratio of volumes or a ratio of distances, which are quantities that are often computed to identify endmembers. This property allows us to easily incorporate abundance estimation within conventional endmember extraction techniques, without incurring additional computational complexity. We use this key property with various endmember extraction techniques, such as N-Findr, vertex component analysis, simplex growing algorithm, and iterated constrained endmembers. The relevance of the method is illustrated with experimental results on real hyperspectral images.

N-FINDR has been widely used for endmember extraction in hyperspectral imagery. Due to its high computational complexity developing fast computing N-FINDR has become interest. One approach is to design field programmable gate array (FPGA) architecture for N-FINDR to reduce computing time. However, two major issues still need to be addressed. One is that the number of endmembers must be fixed regardless of applications. The other is computation of simplex volumes. This paper investigates a progressive version of N-FINDR, previously known as simplex growing algorithm (SGA) for its FPGA implementation which basically resolves these two issues.

Simplex growing algorithm (SGA) was recently developed as an alternative to the N-finder algorithm (N-FINDR) which is shown to be a promising endmember extraction technique. This paper further extends the SGA to a real-time processing algorithm, referred to as real-time SGA (RT SGA) that can effectively address four major issues arising in practical implementation for N-FINDR, (1) use of random initial endmembers which causes inconsistent final results, (2) very high computational complexity which results from an exhaustive search for finding all endmembers simultaneously, (3) requirement of dimensionality reduction because of enormous data volumes to be processed and (4) lack of real-time capability.