Table 1 Reconstruction methods considered
From: High-performance and scalable on-chip digital Fourier transform spectroscopy
Method | Problem |
|---|---|
Pseudoinverse | y=Ax (Moore–Penrose) |
Ridge Regression | \(\mathop {{\min }}_x \left\{ {\left| {\left| {{\bf{y}} - {\bf{Ax}}} \right|} \right|_2^2 + \alpha _2\left| {\left| {\bf{x}} \right|} \right|_2^2} \right\}\) |
LASSO | \(\mathop {{\min }}_x \left\{ {\left| {\left| {{\bf{y}} - {\bf{Ax}}} \right|} \right|_2^2 + \alpha _1\left| {\left| {\bf{x}} \right|} \right|_1} \right\}\) |
BPDN | \(\mathop {{\min }}_x \left\{ {(1/2)\left| {\left| {{\bf{y}} - {\bf{Ax}}} \right|} \right|_2^2 + \alpha _1\left| {\left| {\bf{x}} \right|} \right|_1} \right\}\) |
RBF Network | \(\mathop {{\min }}_c \left\{ {\left| {\left| {{\bf{y}} - {\bf{Ah}}_{\bf{c}}} \right|} \right|_2^2} \right\}\) with \({\bf{h}}_{\bf{c}} = {\bf{Kc}} = \mathop {\sum }\limits_{d = 1}^D c_de^{ - \beta \left| {\lambda - \lambda _d} \right|^2}\) |
Elastic-Net | \(\mathop {{\min }}_{x,x > 0} \left\{ {\left| {\left| {{\bf{y}} - {\bf{Ax}}} \right|} \right|_2^2 + \alpha _1\left| {\left| {\bf{x}} \right|} \right|_1 + \alpha _2\left| {\left| {\bf{x}} \right|} \right|_2^2} \right\}\) |
Elastic-D1 | \(\mathop {{\min }}_{x,x > 0} \left\{ {\left| {\left| {{\bf{y}} - {\bf{Ax}}} \right|} \right|_2^2 + \alpha _1\left| {\left| {\bf{x}} \right|} \right|_1 + \alpha _2\left| {\left| {\bf{x}} \right|} \right|_2^2 + \alpha _3\left| {\left| {{\bf{D}}_1{\bf{x}}} \right|} \right|_2^2} \right\}\) |
