A method of reconstructing a recorded sound field, the method including analysing recorded data in a sparse domain using one of a time domain technique and a frequency domain technique, when using a frequency domain technique, transforming a set of signals, s mic ( t), to the frequency domain using an FFT to obtain s mic; conducting a plane-wave analysis of the recorded sound field to produce a vector of frequency domain plane-wave amplitudes, g plw-cs by solving the following convex programming problem: minimise ‖ g plw − cs ‖ 1 subject to ‖ T plw / mic g plw − cs − s mic ‖ 2 ‖ s mic ‖ 2 ≤ ε 1 where: T plw/mic is a transfer matrix between plane-waves and the microphones, s mic is the set of signals recorded by the microphone array, and ε 1 is a non-negative real number; and when using a time domain technique, analysing the recorded sound field by convolving s mic ( t) with a matrix of filters to obtain a vector of Higher Order Ambisonics: HOA, domain time signals, b HOA ( t), and sampling the vector of HOA-domain time signals over a given time frame, L, to obtain a collection of time samples at time instances t 1 to t N to obtain a set of HOA-domain vectors at each time instant: b HOA ( t 1), b HOA (t 2),..., b HOA ( t N) expressed as a matrix, B HOA by: B HOA = b HOA t 1 b HOA t 2... b HOA t N; and conducting plane-wave analysis of the recorded sound field according to a set of basis plane-waves to produce a set of plane-wave signals, g plw-cs ( t), from G plw which is obtained by solving the following convex programming problem: minimise ‖ G plw ‖ L 1 − L 2 subject to ‖ Y plw G plw − B HOA ‖ L 2 ≤ ε 1, where Y plw is a matrix truncated to a high spherical harmonic order whose columns are the values of the spherical harmonic functions for the set of directions corresponding to some set of analysis plane waves, and ε 1 is a non-negative real number; and obtaining plane-wave signals and their associated source directions generated from the selected technique to enable the recorded sound field to be reconstructed. T plw/mic is a transfer matrix between plane-waves and the microphones, s mic is the set of signals recorded by the microphone array, and ε 1 is a non-negative real number; and when using a time domain technique, analysing the recorded sound field by convolving s mic ( t) with a matrix of filters to obtain a vector of Higher Order Ambisonics: HOA, domain time signals, b HOA ( t), and sampling the vector of HOA-domain time signals over a given time frame, L, to obtain a collection of time samples at time instances t 1 to t N to obtain a set of HOA-domain vectors at each time instant: b HOA ( t 1), b HOA (t 2),..., b HOA ( t N) expressed as a matrix, B HOA by: B HOA = b HOA t 1 b HOA t 2... b HOA t N; and conducting plane-wave analysis of the recorded sound field according to a set of basis plane-waves to produce a set of plane-wave signals, g plw-cs ( t), from G plw which is obtained by solving the following convex programming problem: minimise ‖ G plw ‖ L 1 − L 2 subject to ‖ Y plw G plw − B HOA ‖ L 2 ≤ ε 1, where Y plw is a matrix truncated to a high spherical harmonic order whose columns are the values of the spherical harmonic functions for the set of directions corresponding to some set of analysis plane waves, and ε 1 is a non-negative real number; and obtaining plane-wave signals and their associated source directions generated from the selected technique to enable the recorded sound field to be reconstructed. Y plw is a matrix truncated to a high spherical harmonic order whose columns are the values of the spherical harmonic functions for the set of directions corresponding to some set of analysis plane waves, and ε 1 is a non-negative real number; and obtaining plane-wave signals and their associated source directions generated from the selected technique to enable the recorded sound field to be reconstructed.