FocusedBlindDecon

Geophysicists rely on seismic data to understand the Earth’s subsurface. Data from seismic receivers d{T,2}(nt,nr) contains two types of information convoluted into a single signal: information about the source of the signal (source effects s{T,1}(nts)) and information about the subsurface features it passed through on its way to the receiver (path effects g{T,2}(ntg,nr)). Conventional methods for separating out the two types of information rely on assumptions which may not be completely accurate: extracting source effects requires assumptions about the path, and extracting path effects requires assumptions about the source.

Similarly, in room acoustics, the speech signal s recorded as d at a microphone array is distorted as sound is reverberated due to g i.e., the reflection of walls, furniture and other objects. Speech recognition and compression is simpler when the reverberated records d at the microphones are factorized into the distortions g and the clean speech signal s.

Focused Blind Deconvolution (FBD) performs the above-mentioned factorization and extracts either the source or path information without relying on their assumptions, instead:

• it compares data d from the same source picked up by multiple receivers, and identifies similarities and differences among them;
• similarities among the signals can be identified as source effects s, while dissimilarities indicate path effects g.

FocusedBlindDecon is a Julia package corresponding to the article:

Bharadwaj, Pawan, Laurent Demanet, and Aimé Fournier. "Focused blind deconvolution." 
IEEE Transactions on Signal Processing 67.12 (2019): 3168-3180.

This package uses the fast Fourier transform FFTW.jl on the zero-padded signals in order to perform multi-dimensional cross-correlations and convolutions. After installation, the package has to be initialized either to utilize either of the two packages: IterativeSolvers.jl or Optim.jl, for solving the linear systems. For example, execute one of the following commands.

using FocusedBlindDecon # start import package, also aliased as FBD
FBD.__init__(optg="optim", opts="optim") # uses Optim while solving for g and s
FBD.__init__(optg="iterativesolvers", opts="optim") # uses Optim while solving for s, and IterativeSolvers for g

By default, FBD.__init__() chooses the solvers from IterativeSolvers.jl for optimized performance.

The functionality of this package revolves around the mutable P_fbd type. Firstly, most of the memory necessary to perform a given optimization is allocated while creating an instance of P_fbd, denoted as pa. Then this instance is input to in-place functions (e.g., lsbd!, fbd!, fibd!) which as per Julia convention ends with an exclamation mark, to actually perform the optimizations. Finally, the outputs of the optimizations can be easily accessed from pa e.g., pa[:s] returns the estimated source. Details of these methods are provided in the next section.